Notebook_Week_0.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"week0\"></a>\n",
    "<h1 style=\"color:#00A6D6;\">Week 0: Quantum Information 101</h1>\n",
    "\n",
    "Welcome to the lab exercises in Julia. These notebooks are meant to help you study the material by performing many calculations in an easy and intuitive manner - in short, by playing around!\n",
    "\n",
    "Each notebook consists out of two types of parts:\n",
    "\n",
    "First off, there are parts where Julia is used to make certain calculations and visualize the outcomes: The computer programming makes it possible to calculate and visualize things that are otherwise difficult. You may wish to change the examples, or extend them to perform other calculations that help you become familiar with the material in our class and beyond. \n",
    "\n",
    "Secondly, each notebook has a few homework exercises marked \"edX Exercises\". These are calculations that we would definitely like you to perform. The answers to these need to be entered into the edX system, they are graded as part of the course. Completion of these exercises accounts for 20% of the total course completion.\n",
    "\n",
    "### If you have never used a Julia sheet before, we recommend you to begin with the \"Getting Started\" notebook. \n",
    "\n",
    "Ready? Then let's get started! Click shift-enter in the box below to load the first snippet of Julia!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# load functions/globals used throughout the notebook\n",
    "include(\"source/main.jl\") ;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the line above will make the Julia compiler compile several packages. After compiling them it will print several info and warning messages."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* <a href=\"#single_qubit\"> The Single Qubit </a>\n",
    "\n",
    "* <a href=\"#two_qubits\"> Two Qubits </a>\n",
    "\n",
    "* <a href=\"#measurements\"> Measurements </a>\n",
    "\n",
    "* <a href=\"#transformations\"> Unitary Transformations </a>\n",
    "\n",
    "* <a href=\"#bloch_sphere\"> Bloch Sphere </a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------\n",
    "<a id=\"single_qubit\"></a>\n",
    "<h2 style=\"color:#00A6D6;\">The Single Qubit</h2>\n",
    "\n",
    "Let's start with a single qubit! As you've learned in the videos - and you may want to recap with the lecture notes - the word qubit refers to a quantum bit. \n",
    "\n",
    "Throughout we will use the bra-ket notation, the quantum information way of writing down vectors. Let's remember what the two vectors corresponding to the two classical bits 0 and 1 look like.\n",
    "\n",
    "$$\\left| 0 \\right\\rangle := \\begin{pmatrix}1 \\\\ 0\\end{pmatrix}, \\quad \\text{and} \\quad \\left| 1 \\right\\rangle := \\begin{pmatrix}0 \\\\ 1\\end{pmatrix}.$$\n",
    "\n",
    "Let's define them in Julia:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Int64,1}:\n",
       " 1\n",
       " 0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The vector corresponding to |0>\n",
    "v0 = [1; 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Int64,1}:\n",
       " 0\n",
       " 1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The vector corresponding to |1>\n",
    "v1 = [0; 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Accordingly, we can describe the state $\\left| \\psi \\right\\rangle$ of a qubit in general by\n",
    "\n",
    "$$\\left| \\psi \\right\\rangle = \\alpha \\left| 0 \\right\\rangle + \\beta \\left| 1 \\right\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix} \\:.$$\n",
    "\n",
    "The parameters $\\alpha$ and $\\beta$ are amplitudes. Let's try constructing such a vector for some values of $\\alpha$ and $\\beta$ in Julia:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 0.707107\n",
       " 0.707107"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Amplitudes\n",
    "alpha = 1/sqrt(2); # note, by ending a line with a semi-colon output is supressed\n",
    "beta = 1/sqrt(2);  # try adding a semi-colon to the last line of this cell to see what happens\n",
    "\n",
    "# The qubit psi corresponding to such amplitudes\n",
    "psi = alpha * v0 + beta * v1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "<a id='normalization'></a>\n",
    "<h4 style=\"color:#00A6D6;\">Normalization</h4>\n",
    "\n",
    "Remember that for $\\left| \\psi \\right\\rangle$ to be a valid qubit we require $\\left| \\psi \\right\\rangle$ to be normalized. For the inner product of $\\left| \\psi \\right\\rangle$ with itself&mdash;in bra-ket notation as $ \\langle \\psi \\:|\\: \\psi \\rangle$&mdash;it must be that\n",
    "\n",
    "$$ \\langle \\psi \\:|\\: \\psi \\rangle = \\lvert\\alpha\\rvert^2 + \\lvert\\beta\\rvert^2 = 1$$\n",
    "\n",
    "To make this more explicit recall that a bra $\\left\\langle \\psi \\right|$ denotes the complex conjugate of the ket $\\left| \\psi \\right\\rangle$:\n",
    "\n",
    "$$\\left\\langle \\psi \\right|:= \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix}^{*T} = \\begin{pmatrix} \\alpha^* , \\beta^* \\end{pmatrix} \\:.$$ \n",
    "\n",
    "Let's expand this in terms of the vector: \n",
    "\n",
    "$$\\langle \\psi \\:|\\: \\psi \\rangle = \\begin{pmatrix} \\alpha^*\\:, \\beta^* \\end{pmatrix} \\cdot \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix} = \\alpha \\cdot \\alpha^* + \\beta \\cdot \\beta^* = \\lvert\\alpha\\rvert^2 + \\lvert\\beta\\rvert^2 = 1$$\n",
    "\n",
    "Let's check whether the qubit psi we have defined above is normalized!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1x2 Array{Float64,2}:\n",
       " 0.707107  0.707107"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In Julia, this gives us the bra of a vector. Let's print it\n",
    "psi'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Float64,1}:\n",
       " 1.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's now check normalization!\n",
    "psi' * psi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Be careful that the bra is the <b>conjugate</b> transpose - and not merely the transpose! To see this, let's construct a complex vector, where \"im\" is the Julia way of writing the complex i."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Complex{Float64},1}:\n",
       " 0.707107+0.0im     \n",
       "      0.0+0.707107im"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's define a complex vector\n",
    "alpha = 1/sqrt(2);\n",
    "beta = im * 1/sqrt(2);\n",
    "\n",
    "# Let's display the vector\n",
    "psi = alpha * v0 + beta * v1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1x2 Array{Complex{Float64},2}:\n",
       " 0.707107-0.0im  0.0-0.707107im"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# And let's display it's bra: the complex conjugate\n",
    "psi'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an exercise for yourself, go and adapt the Julia code below to test whether $$|\\Psi\\rangle = \\alpha |0\\rangle + \\beta |1\\rangle$$ with $\\alpha = 1/3$ and $\\beta = 2/3$ is normalized! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[9], in expression starting on line 2",
     "output_type": "error",
     "traceback": [
      "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[9], in expression starting on line 2",
      ""
     ]
    }
   ],
   "source": [
    "# First, let's define again the amplitudes\n",
    "alpha = ...;\n",
    "beta = ...;\n",
    "\n",
    "# Construct the vector psi\n",
    "psi = alpha * v0 + beta * v1;\n",
    "\n",
    "# Compute the inner product <psi|psi>\n",
    "psi'*psi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "<h4 style=\"color:#00A6D6;\">A real valued example</h4>\n",
    "\n",
    "Remember that $\\alpha$ and $\\beta$ are in general complex numbers! Let us however assume here that $\\alpha$ and $\\beta$ have a real value</b>. The normalization condition thus becomes $\\alpha^2 + \\beta^2 = 1$. \n",
    "\n",
    "To visualize such a qubit, let us make the following parametrization \n",
    "\n",
    "$$\\alpha = \\cos\\theta \\quad \\text{and} \\quad \\beta = \\sin\\theta$$\n",
    "\n",
    "and see how the state vector can be represented in a 2D plot.\n",
    "\n",
    "<b> click in the code block below and press shift+enter, it might take a moment before the resulting image is loaded</b>.\n",
    "\n",
    "You will see a slider appear which lets you set $\\theta$. You will see a plot of the corresponding state vector appear. \n",
    "\n",
    "$$\\left| \\psi(\\theta) \\right\\rangle = \\alpha \\left| 0 \\right\\rangle + \\beta \\left| 1 \\right\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix} \\:.$$\n",
    "\n",
    "Use the slider and vary $\\theta$, you will see the state vector representation vary accordingly. As an exercise for yourself, go and investigate the angles for the elements $|0\\rangle$ and $|1\\rangle$ of the standard basis, and the vectors defining the Hadmard basis:\n",
    "\n",
    "$$|+\\rangle = \\frac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle).$$\n",
    "\n",
    "$$|-\\rangle = \\frac{1}{\\sqrt{2}}(|0\\rangle - |1\\rangle).$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "Interact.Slider{Int64}(Signal{Int64}(0, nactions=0),\"θ\",0,-180:15:180,true)"
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     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7fd540092e90>)"
      ]
     },
     "execution_count": 10,
     "metadata": {
      "comm_id": "1efd1d20-9d68-4115-baa3-2b623461fc35",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "single_state_vector_plot() # load the interactive plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have already seen above how to express $|+\\rangle$ and $|-\\rangle$ in terms of the standard Basis $|0\\rangle$, $|1\\rangle$ above. Since the Hadmard basis is also a basis, we should of course also be able to write $|0\\rangle$ and $|1\\rangle$ in terms of $|+\\rangle$ and $|-\\rangle$. \n",
    "\n",
    "Can you guess by looking at the picture above? Go and find the coefficients $\\alpha_0, \\beta_0$ and $\\alpha_1,\\beta_1$ visually:\n",
    "\n",
    "$$|0\\rangle = \\alpha_0 |+\\rangle + \\beta_0 |-\\rangle$$\n",
    "$$|1\\rangle = \\alpha_1 |+\\rangle + \\beta_1 |-\\rangle$$.\n",
    "\n",
    "Verify your answers using the Julia code below!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[42], in expression starting on line 6",
     "output_type": "error",
     "traceback": [
      "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[42], in expression starting on line 6",
      ""
     ]
    }
   ],
   "source": [
    "# Let's first define the plus and minus state\n",
    "plus = 1/sqrt(2) * (v0 + v1);\n",
    "minus = 1/sqrt(2) * (v0 - v1);\n",
    "\n",
    "# Let's first make the v0 vector by combining plus and minus\n",
    "alpha0 = ...;\n",
    "beta0 = ...;\n",
    "newV0 = alpha0 * plus + beta0 * minus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[43], in expression starting on line 2",
     "output_type": "error",
     "traceback": [
      "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[43], in expression starting on line 2",
      ""
     ]
    }
   ],
   "source": [
    "# And then the new one vector\n",
    "alpha1 = ...;\n",
    "beta1 = ...;\n",
    "newV1 = alpha1 * plus + beta1 * minus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\">edX Exercise 1</h3>\n",
    "\n",
    "We're now ready for the first edX Exercise - the result of which you need to enter into the edX grading forms. Consider $$\\left| b_0 \\right\\rangle = \\sqrt{\\frac{1}{3}} \\left| 0 \\right\\rangle + \\sqrt{\\frac{2}{3}} \\left| 1 \\right\\rangle$$\n",
    "\n",
    "What real-valued vectors are orthogonal to this vector? In other words given $\\left| b_0 \\right\\rangle$ which $\\left| b_1 \\right\\rangle$ satisfy\n",
    "\n",
    "$$ \\left\\langle b_1 | b_0 \\right\\rangle = 0 \\:?$$\n",
    "\n",
    "<b>Your task is to find parameters $\\alpha_1 \\geq 0$ and $\\beta_1$ such that\n",
    "\n",
    "$$\\left| b_1 \\right\\rangle = \\begin{pmatrix} \\alpha_1 \\\\ \\beta_1 \\end{pmatrix}$$\n",
    "\n",
    "is orthogonal to $\\left| b_0 \\right\\rangle$ </b>.\n",
    "\n",
    "Take a guess, use Julia to find the vector for you, or compute it by hand! By clicking in the code box just below you can fill in values for $\\alpha_1$ and $\\beta_1$ and calculate $ \\left\\langle b_1 | b_0 \\right\\rangle$ to see how you are doing.\n",
    "\n",
    "To start you off we have set $\\alpha_1$ and $\\beta_1$ to $\\sqrt{\\frac{1}{2}}$ and $\\sqrt{\\frac{1}{2}}$ respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You have entered |b_1> = \n",
      "0.7071067811865476 ⋅|0> + 0.7071067811865476 ⋅|1> \n",
      "\n",
      "The inner product is \n",
      "  < b_0 | b_1 > = \n",
      "[0.9855985596534889]\n"
     ]
    }
   ],
   "source": [
    "# First let's define the vector b0. We'll do this directly as a vector now\n",
    "b0 = [sqrt(1/3) ; sqrt(2/3)];\n",
    "\n",
    "# Set the amplitudes for b1. We'll put some funny amplitudes to start with...\n",
    "alpha1 = sqrt(1/2);\n",
    "beta1 = sqrt(1/2);\n",
    "\n",
    "b1 = [alpha1; beta1]\n",
    "###### \n",
    "println(\"You have entered |b_1> = \")\n",
    "println(\"$alpha1 ⋅|0> + $beta1 ⋅|1> \\n\")\n",
    "println(\"The inner product is \\n  < b_0 | b_1 > = \")\n",
    "println(b0'*b1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\">edX Exercise 2</h3>\n",
    "\n",
    "Calculate the exact inner product of $$|+\\rangle$$ and $$|0_y\\rangle = \\frac{1}{\\sqrt{2}}(|0\\rangle + i |1\\rangle)\\:.$$ \n",
    "\n",
    "In other words, calculate \n",
    "\n",
    "$$ \\langle 0_y | + \\rangle$$\n",
    "\n",
    "<b> Note: $|0_y\\rangle$ is complex valued. </b>\n",
    "\n",
    "<h4 style=\"color:#00A6D6;\"> Supplement to Exercise 2</h4>\n",
    "\n",
    "Below, you can enter the states $\\lvert+\\rangle$ and $|0_y\\rangle$ in terms of coefficients $\\alpha_1$, $\\beta_1$ and $\\alpha_2$, $\\beta_2$:\n",
    "\n",
    "$$ \\lvert+\\rangle = \\begin{pmatrix} \\alpha_1 \\\\ \\beta_1 \\end{pmatrix} \\quad \\lvert0_y\\rangle = \\begin{pmatrix} \\alpha_2 \\\\ \\beta_2 \\end{pmatrix} $$ \n",
    "\n",
    "Note, in Julia, when it comes to complex numbers, one writes <pre> im </pre> instead of $i$. \n",
    "\n",
    "\n",
    "Thus $ z := x + i \\cdot y $ translates to Julia code\n",
    "\n",
    "<pre>\n",
    "z = x + im*y\n",
    "</pre> \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: UndefVarError: .. not defined\nwhile loading In[45], in expression starting on line 5",
     "output_type": "error",
     "traceback": [
      "LoadError: UndefVarError: .. not defined\nwhile loading In[45], in expression starting on line 5",
      ""
     ]
    }
   ],
   "source": [
    "# |+> state\n",
    "# replace the dots \"..\" with the appropriate coefficient\n",
    "# we have filled in a value for β_2\n",
    "# to show you how to fill in \"im\" times the square root of a fraction.\n",
    "α_1 = .. \n",
    "β_1 = ..\n",
    "\n",
    "plus = [α_1; β_1];\n",
    "\n",
    "# |0>_y state\n",
    "# replace the dots \"..\" with the appropriate coefficient\n",
    "α_2 = ..\n",
    "β_2 = im*sqrt(1/2)\n",
    "\n",
    "y0 = [α_2; β_2];\n",
    "\n",
    "# Compute the inner product - your code goes below!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------\n",
    "<a id=\"two_qubits\"></a>\n",
    "<h2 style=\"color:#00A6D6;\">Two Qubits</h2>\n",
    "\n",
    "Of course we will generally have more than one qubit! Remember the rule for combining the state of two distinct qubits into a two qubit state. Let $$\\lvert \\psi_i \\rangle = \\alpha_i \\left| 0 \\right\\rangle + \\beta_i \\left| 1 \\right\\rangle = \\begin{pmatrix} \\alpha_i \\\\ \\beta_i \\end{pmatrix} $$\n",
    "\n",
    "describe the state of the $i$-th qubit. \n",
    "\n",
    "We can describe the state of two qubits by taking the tensor product\n",
    "\n",
    "$$\\left| \\psi_1 \\right\\rangle \\otimes \\left| \\psi_2 \\right\\rangle = \\Big(\\alpha_1 \\left| 0 \\right\\rangle + \\beta_1 \\left| 1 \\right\\rangle \\Big) \\otimes \\Big(\\alpha_2 \\left| 0 \\right\\rangle + \\beta_2 \\left| 1 \\right\\rangle \\Big) =$$\n",
    "\n",
    "$$\\begin{pmatrix} \\alpha_1 \\\\ \\beta_1 \\end{pmatrix} \\otimes \\begin{pmatrix} \\alpha_2 \\\\ \\beta_2 \\end{pmatrix} = \\begin{pmatrix} \\alpha_1 \\begin{pmatrix} \\alpha_2 \\\\ \\beta_2 \\end{pmatrix}  \\\\ \\beta_1 \\begin{pmatrix} \\alpha_2 \\\\ \\beta_2 \\end{pmatrix}  \\end{pmatrix} = \\begin{pmatrix} \\alpha_1 \\cdot \\alpha_2 \\\\ \\alpha_1 \\cdot \\beta_2  \\\\  \\beta_1 \\cdot \\alpha_2 \\\\ \\beta_1 \\cdot \\beta_2 \\end{pmatrix}  $$\n",
    "\n",
    "To illustrate this, let us calculate the vector associated with $ \\left| \\psi_1 \\right\\rangle \\otimes \\left| \\psi_2 \\right\\rangle$ given $\\left| \\psi_1 \\right\\rangle$ and $\\left| \\psi_2 \\right\\rangle$.\n",
    "\n",
    "<b> click in the code block below and press shift+enter to see the results</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Int64,1}:\n",
       " 0\n",
       " 1\n",
       " 0\n",
       " 0"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's first define the vectors, adapt the amplitudes to play around!\n",
    "\n",
    "# Define Psi1\n",
    "alpha1 = 1;\n",
    "beta1 = 0;\n",
    "psi1 = [alpha1; beta1];\n",
    "\n",
    "# Define Psi2\n",
    "alpha2 = 0;\n",
    "beta2 = 1;\n",
    "psi2 = [alpha2; beta2];\n",
    "\n",
    "# Compute the tensor product\n",
    "psiTwo = kron(psi1,psi2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\">edX Exercise 3</h3>\n",
    "\n",
    "Consider the following tensor product\n",
    "\n",
    "$$ |0_y\\rangle \\otimes | + \\rangle = \\begin{pmatrix} c_1 \\\\ c_2 \\\\ c_3 \\\\ c_4 \\end{pmatrix} $$\n",
    "\n",
    "Calculate the coefficients $c_1$, $c_2$, $c_3$, $c_4$. \n",
    "\n",
    "Note, $|0\\rangle_y$ has been defined in exercise 2.\n",
    "\n",
    "<h4 style=\"color:#00A6D6;\"> Supplement to Exercise 3 </h4>\n",
    "\n",
    "Similar to the previous exercise you can check if your calculations went well using the code block just below :\n",
    "\n",
    "You can enter the states $|0_y\\rangle$ and $|+\\rangle$ numerically in terms of coefficients $\\alpha_1$, $\\beta_1$ and $\\alpha_2$, $\\beta_2$ and calculate the associated tensor product."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: UndefVarError: .. not defined\nwhile loading In[47], in expression starting on line 5",
     "output_type": "error",
     "traceback": [
      "LoadError: UndefVarError: .. not defined\nwhile loading In[47], in expression starting on line 5",
      ""
     ]
    }
   ],
   "source": [
    "# |0_y> state\n",
    "# replace the dots \"..\" with the appropriate coefficient\n",
    "# we have already filled in a correct value for β_1\n",
    "# to demonstrate the syntax.\n",
    "α_1 = ..\n",
    "β_1 = im*sqrt(1/2)\n",
    "\n",
    "y0 = [α_1; β_1];\n",
    "\n",
    "# |+> state\n",
    "# replace the dots \"..\" with the appropriate coefficient\n",
    "α_2 = ..\n",
    "β_2 = ..\n",
    "z0 = [α_2; β_2];\n",
    "\n",
    "# Compute the tensor product using the kron function\n",
    "kron(y0,z0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----\n",
    "<a id=\"measurements\"></a>\n",
    "<h2 style=\"color:#00A6D6;\">Measurements</h2>\n",
    "\n",
    "Let's now measure some qubits! Chiefly, we will be measuring one - or more - qubits in a basis, where we will write the basis vectors as $|b_j\\rangle$ for outcome \"j\". We saw in the lecture that the probability of obtaining a particular outcome is given by\n",
    "\n",
    "$$P(B=j) := \\lvert \\langle \\psi \\:|\\: b_j \\rangle \\rvert^2 $$\n",
    "\n",
    "<h4 style=\"color:#00A6D6;\">Measuring a real-valued qubit</h4>\n",
    "\n",
    "To gain some intuition, let us now again consider a qubit with real valued amplitudes. Remember, that we can parameterize such a qubit by an angle $\\theta$\n",
    "\n",
    "$$\\left| \\psi(\\theta) \\right\\rangle = \\cos\\theta \\left| 0 \\right\\rangle + \\sin\\theta \\left| 1 \\right\\rangle = \\begin{pmatrix} \\cos\\theta \\\\ \\sin\\theta \\end{pmatrix} \\:.$$\n",
    "\n",
    "Let's now assume the basis that we measure in is also real valued where the outcome j=0 corresponds to the vector \n",
    "\n",
    "$$\\left| b_0 \\right\\rangle = \\begin{pmatrix} \\cos\\gamma \\\\ \\sin\\gamma \\end{pmatrix} \\:.$$\n",
    "\n",
    "Let us visualize $\\lvert \\psi \\rangle$ and $\\lvert b_0 \\rangle$ and calculate the corresponding $p_{b=0}$.\n",
    "\n",
    "<b> Click in the code block below and press shift+enter, it might take a moment before the resulting image is loaded</b>.\n",
    "\n",
    "You will see a sliders appear which lets you set $\\theta$ and $\\gamma$ (in degrees).\n",
    "\n",
    "A plot will appear of $\\lvert \\psi \\rangle$ and $\\lvert b_0 \\rangle$ - the solid part corresponds to the projection $ \\big| \\langle b_0 | \\psi \\rangle \\big| \\lvert b_0 \\rangle$ - with $P_{B=0}$ written in the title.\n",
    "\n",
    "Play around with the values of $\\theta$ and $\\gamma$ and see if you can understand what is going."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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JnRAJcLlc2NjYIDk5me1QCCGkVpTYCZEAn89HSkoK2rVrx3YohBBSK0rshEjg7Nmz8PLyYjsMQggRiW53I0QCBw4coIVqCCEqjXrshIjpn3/+QevWrWFkZMR2KIQQIhIldkL+H4/Hq/NBL9u3b4efn58SIyKEEMnRUDzRehcvXsTu3bsRExOD3NxcuLq6ws7ODrt27RIcU1JSgoyMDNjZ2bEYKSGE1I8SO9F6AwcOxMCBA+s85tChQ5gwYYKSIiKEEOlRYidEDGfPnsW5c+fYDoMQQupF19iJVmIYRuxjb9y4ARcXF3C59HEhhKg+OlMRrWRqair2sefOncP06dMVGA0hhMgPh5Gk60IIIYQQlUY9dkIIIUSDUGInhBBCNAgldkIIIUSD0O1uRGMVFxcjMzMTmZmZyMvLQ1FRkeBPcXGx0L+rqqrA5/MFfzgcDrhcLnR0dKCjowNjY2OYmJgI/v7w302bNoWlpSWsrKzQqFEjtl820SLp6enIy8tjOwyiRM2aNYO1tXWdx9DkOaKW3r59i7S0NGRmZuLly5d4+fKl4N/Vf797965GOUNDQ6HkbGJiAiMjI+jr64PL5YLL5YLD4YBhGEGSr6qqEnwR+PALQUlJSY36jY2NYWVlJUj0H/9tbW2NZs2aKeO/iGi49PR02Nvbo7S0lO1QiBIZGhri6dOndSZ36rETlffmzRskJCTg3r17iI+PR3x8PF68eCHYz+Vy0bJlS0EC7du3b42E2rx5cxgbG0NHR0ducfH5fJSUlCA3N1cwMvDhF4ukpCRERUUhKysLVVVVgnIWFhZwdHRE165d4ejoCEdHR7Rs2VJucRHtkJeXh9LSUhw6dAj29vZsh0OU4OnTp5gwYQLy8vIosRP1UVcSNzExQZcuXTBixAh06dIF7dq1g6WlJVq2bAldXeW/lblcrqDX37ZtW5HH8Xg85OTkIDMzE6mpqUhISEB8fDyCg4ORn58PgJI9kZ69vT26dOnCdhhEhVBiJ6wpKCjAvXv3RCZxR0dHjBgxQpDobG1t1XL1Nx0dHbRq1QqtWrVC165dMWrUKAD/rn6XlpaG+Ph4wf9BXcneyckJ5ubmbL4UQogaoMROlCopKQmhoaEIDQ1FbGws+Hy+SiZxX19f7N27V6FtcDgc2NjYwMbGBiNGjABQf7J3cnKCp6cnvLy80KlTJ3A4HIXGSAhRP5TYiUJVVVXh1q1bgmSelJQEAwMDDBgwADt27EDv3r1ZT+K1cXNzY6XdupJ9TEwMwsLC8Msvv2DFihWwtraGl5cXPD090adPH+jr67MSMyFEtVBiJ3JXVFSES5cuISwsDOfPn8ebN2/QokULeHp6Yv369ejXrx8MDQ3ZDrNOY8eOZTsEgQ+T/YQJE1BRUYHo6GiEhoYiLCwMW7duhYmJCQYOHAgvLy8MHjwYTZo0YTtsQghLKLETucjIyEBYWBhCQ0Nx9epVVFRUoGPHjpg5cyY8PT3h5OSkcr1ydaWvr48BAwZgwIAB2Lx5Mx4+fCgYEZk4cSJ0dHTg4uICLy8veHl54dNPP2U7ZEKIEtF97ERqBQUF2LdvHw4cOID79+9DV1cXvXv3FgwPt2nThu0Qtc6rV69w/vx5hIaGIiIiAmVlZbCzs8O4ceMwbdo0tGrViu0QiZwkJCTA0dER8fHxNCteS4j7O6cuFJFYfHw8pkyZAgsLCyxZsgSfffYZjh49iry8PERERGDevHlqn9RjYmLYDkEqFhYW+OabbxAWFoa8vDycOXMG3bp1Q0BAAKytrTF69GhER0dL9Dx6Qoh6ocROxPL+/Xvs378fX375Jbp27YrIyEisWLECGRkZOHbsGEaPHi3RM85VXVBQENshyMzIyAhDhw7F3r17kZmZiQ0bNuDBgwfo06cP/vOf/2Dbtm0oLCxkO0xCiJxRYid1Sk5OxuLFi2FlZYXJkyejSZMmCA0NRUpKCpYtW4YWLVqwHaJCHD16lO0Q5Kpx48aYN28enj59isjISNjb22P+/PmwsLDArFmz8PDhQ7ZDJEQrnDp1Cps3b1ZoG5TYSQ08Hg9hYWEYNGgQbG1tsWfPHvj6+uLZs2cIDw+Hp6enXJdmVUWqPmtfWhwOB3379sXJkyeRlpaGRYsW4ezZs+jUqRNcXV0REhKC8vJytsMkRGO5u7tj7969Cr0cRomdCOTk5GDdunVo27YtvLy88ObNG8Ew7vr162Fra8t2iHJRWVmJ7Oxs8Hg8oe3379+v0XMtLS3F7du3UVxcrMwQlcLS0hKrVq1CWloaTpw4AT09PYwbNw7W1tb473//i/T0dLZDJETjGBkZwc3NDadOnVJYG5TYCbKysuDn5wcrKyusXr0a/fr1Q1xcHOLi4jB58mQ0bNiQ7RDrxePx8PLlyxrfghcuXIidO3cKbXv69Cm+//77GteXU1JSkJGRIbStpKQEkZGRNZ4UFxwcjCVLltQ49qeffkJqaqqsL0ep9PT0MHLkSERFReHx48cYPXo0tm7dijZt2mD8+PFITk5mO0RCWFNZWSn3OufMmYOtW7fKvV4Bhmitt2/fMsuXL2cMDQ0ZMzMzZt26dcybN2/YDqte8fHxzN9//y20LTY2lpkxYwbz/v17oe3l5eVStbFo0SKJy1RUVDB37txhcnJyhLbv2LGDWbBggVRxsKWoqIjZtm0b06pVK0ZXV5eZPXs28/r1a7bDIh+Ij49nADDx8fFsh6IS5s2bx2RnZ8u1zpCQEGbfvn0SlVmxYgXz119/1Xvc6NGjmXv37klUt7i/c0rsWuj9+/fM+vXrmSZNmjANGzZkli1bxhQUFLAdVg3FxcVMREQEU1FRIbR9165dzJ07dxTa9ubNm+VaH4/HE/o5Pz+fGTx4sMqflEtKSpiAgACmcePGjJGREfPDDz8w7969YzsswlBi/9jkyZOZtLQ0sY+fP39+nfsjIiKYb7/9VuT+Fy9eMDNmzGCWLFnCjBo1iikuLmYYhmHKysqYAQMGMCkpKXXWf/PmTWb8+PFix8swlNhJLSorK5k9e/YwVlZWjI6ODjNjxgwmMzOT7bAEqj8Y1Z48ecL88ssvNbZrssDAQCYwMJDtMGrIz89n/P39GQMDA6Zp06bMxo0ba4yOEOWixC5MksT++vVrZtWqVSL3v337lnFycmLKyspq3Z+amso4OjoKRuc2bNjAzJs3T7D/2bNnjIuLC8Pn8+uMw9XVlcnKyhIrZoYR/3dO19i1AMMwOH36NDp16oSpU6eiR48eePr0KXbs2AELCwu2wwMArF69Grt27RLaZm9vj0WLFsHIyIilqJTP398ffn5+QtvS0tJw5MgRlJWVsRQVYGZmhsDAQDx//hzDhw/H4sWL0b59e+zbt6/GJERCVF1UVBS++uorkfvXrFmDr7/+Gg0aNKixr7KyEiNHjsT8+fPRvHlzAIC1tTXOnj0rOMbW1hbW1tYICQmpMw4/Pz9s2bJFylchGiV2DRcdHY0ePXpg+PDhsLKywr1793Ds2DHW1g8vLy/HunXrcO/ePaHtK1aswIIFC1iJSdUYGxsL/dyoUSNUVFSoxGpxlpaW2LlzJx4/fgxnZ2f4+vri888/R2hoqErER4g4bt++je7du9e6r7S0FLt378aECRNq3b9p0yZkZ2dj3Lhxgm3v3r1DRkaG0JfcefPmYe3atXXGMXLkSFy4cEHut5hSYtdQ9+/fx+DBg9GnTx9UVVUhIiICly9fhqOjo1Lj+Phkr6+vjx49euDzzz9XahySSkxMZDsEATMzsxp3JzAMAx8fH1y4cIGVmNq3b48TJ04gLi4OLVq0wNChQ+Hq6qq2S/ES7VJRUQE9Pb1a94WFhaFdu3Zo3LhxjX3l5eUICgrCtGnThNbyePToEQCAz+cLtjk7O+Ply5d48uSJyDh0dXUxZswYHDhwQNqXUnu9cq2NsK6goADfffcd9u3bh88++wwnTpzAiBEjwOFwlB7L7du3sXr1apw5c0bwrHAOh4PevXsrPRZJ+fv7IzQ0lO0wROJwODh+/DiqqqqEtr9+/Rrm5uZKe5Kek5MTIiIicOXKFSxduhSurq4YOnQotm3bBktLS6XEQCTDVJaCl/9c6e3qNLEFR095Cz+lp6dj/fr1SE1Nxbhx4wSPYk5PTxc8y6KiogKOjo4YO3Ysli9fDgCIjIxEjx49aq0zJCQE+fn58PHxEdoeGxsLExMToS8LXC4X3bt3x8WLF9GhQweRcU6fPh3u7u745ptvZHq9H6LErkHCwsIwY8YMlJaWYvv27Zg2bRp0dZX3K37//r1Qr7Jr1644f/48K18qZKXQe0zl6OPfb3h4ODIyMrBixQqlxcDhcODm5ob+/fvj+PHj+O677+Dg4IDg4GB8/fXXavn712S8/OcoOuyu9HZNxl+CbotOSmsvICAAwcHB2LFjBwIDAwWJPTIyUuj6enl5OW7evCn4OSEhATNmzKi1zjNnzsDAwAALFy4EwzDgcDioqKhAQkICXFxcahzv4OCA+/fv1xmnmZkZunbtioiICPTv31+al1oDJXYNUFBQgPnz5+PgwYMYMmQIfv/9d6X3lnbu3Ink5GQEBgYKtinzS4W8WVtbsx2CVHx9fWtse/36NUxMTBQ+CZHL5WLMmDFwc3PDggULMHnyZJw4cYKV9yMRTaeJLUzGX2KlXWW5c+cOevToAT09PURERAjNKYqPj8fkyZMB/HtpMDg4GCdPnhTsT0tLq3UYnmEYXL9+HcOHD8fBgwcF28PDwxEVFYW+ffvWKGNmZib0pUEUhmHkOglVfc+8aszf3x+LFi2Cubm5zHV92Evft2+f0npIPB5P6BrT9OnTFd4mkc7z58+xf//+GncdKEqTJk1w4MABjBo1CtOnT1fb3rs8P6eqhKNnqNSeMxtsbGzQuXNnZGdnIzw8HH/++adgH4/HE3ofWlpawsnJSfDzu3fvak3sL1++xNu3b9GtWzeh7RcuXACHw8GIESNqlGnSpEmNVSs/lp+fj7t372L79u1iv7760OQ5Fnh7e+P333+XqY6CggJ8/fXX8PLyQpcuXfD48WNMmjRJKSfO1atX49dff1V4O0Q+evbsWSOpl5eXC030UQRPT088fvwYXl5emDx5Mjw9PZGZmanQNuVJHp9Two4WLVqgQYMGOHnyJBo2bIiBAwcC+HdSrJ2dndCxd+/exbBhwwQ/czicWj8b2dnZACB0vZzH4+HEiRNwdXXFf/7znxpluFxuvT3x33//Xa7X1wFK7Kzo0aMH7ty5I/WJNSwsDA4ODggNDcW+ffsQFham1KHO5cuXY9GiRUprjw0fXlLQRA8ePICnp2eNyXfyVt17Dw0NRXx8PBwcHLB//361uDVO1s8pYV9sbCycnZ0Fk9o+HjIvLy9HRkaG0OOnGzdujPz8/Bp16erqgsPhoGXLloJtFy5cQG5uLn7++eda23/z5g1MTU1FxldVVYWQkBBMmjRJ4tdWF0rsLBk6dChOnz4tUZkPe+lffPGFUnrphw4dqtHbU+dr5+IqLS1lOwSFcnZ2RlhYmNJ+l+rae5fmc0pUR3FxMczMzAQ/P3z4EB07dgTw73XtNWvW4NtvvxUq06ZNm1oTe/W8mw8/Mxs3bsT06dPRs2fPWtvPz8+HjY2NyPiOHz8ODw8PGBgYiP2axEGJnSXjx4/HoUOHxD7+4176uXPnlNJLt7e3l/u3SXXw448/sh2Cwn18S9ydO3ewbt06hfXi1bH3LunnlKiW0aNHIzo6Gq9fvxbanpOTA39/f3z99dc1etQ9e/as9d7zJk2aoFu3boI1Lv744w9UVFQgODhYZPtJSUno0qWLyP1bt27FnDlzJHlJYqHELoKiV0EzNDSEjY1NvQuhvH37Vmm99MrKyhqPHHV0dBTcg040m7OzM5ydnYUmRSrCx713Dw8PZGVlSV2fIj+r4n5OiWoaP348NmzYgPHjx2PixIl48eIF1q5di8OHD2PVqlWwta05U3/gwIGIjo6utb6dO3di586d8PPzw99//42rV6+KPD8yDIOYmJhaZ8sD/14maNvhmr8AAAAgAElEQVS2rWKW9RZ79Xkt4+vrq/A2EhMTmTlz5ojc/+TJE+bTTz9lTE1NmX379tX7QAFZff/998zp06cV2gZRL0VFRUxlZaXC6g8NDWVatmzJtGzZkrl586ZUdUjyWT1+/LjE9df3OWULPQRGWH0PgdmyZQvz+PHjeuspLy9nmjVrJtHDWWpz7949xtbWVuT+kSNHMnfv3pWoTnoIjBpo3749Xr16hZKSkhr7zp49iy+//BL6+vq4d++eUma8//TTT/D29lZoG+oiLy+P7RBUwoMHDzB69GiFDZd7enrir7/+Qrt27dC7d2/s3r1bIe1Uk2YJ3ro+p0R9PHr0qM4V4Krp6+tj9uzZdQ6xi2Pbtm0iR5PS0tKQm5uLrl27ytSGKJTYWTZx4kShdYL5fD5+/PFHeHt7o3///rh161atw0WySk5Oplt56jBlyhS2Q1AJLi4uOHHihEK/VLZs2RJRUVGYMmUKvvnmG8yePRsVFRUKaUva1/Hx55SoH0l+94sXL8aFCxfqvQddlPT09DpXsNu8eTPmzp0rVd3ioMTOMi8vL4SFhQEACgsLMXz4cKxatQo//fQTTp48CRMTE4W0+88//4i89kOAVatWsR2Cyvh4kl1CQgLevn0r1zb09fWxY8cO7NixA7t27UL//v2Rk5Mj1zZk8eHnlKifx48fS/TgKSMjI+zcuVOq+8t5PB5mz56N/fv313rXSXFxMSIjIzF8+HCJ6xYXJXaWcblc2NjYIDIyEt26dUNUVBRCQ0Px/fffK/RBHoMHD2bt0a3qoK6ZrNqurKxMIc+QBoAZM2bg6tWrSEpKgqOjI+Lj4xXSjqSqP6fJyclsh0JEMDU1FXnbmIODA2bOnClRfV9++SWmTp0q8XMj1q5diwULFoj8InHx4kVMnTpVoaNgmn9Dsorj8/mIi4vDkSNH0KJFC8TFxdVYGUlWWVlZWLNmDYKDgxU+45lovh49eoh8+pU8uLi44N69exg+fLhg1TxRz8aWlLRzBfh8PlJSUtCuXTu5xEHkb9OmTXKv093dHe7ukj0wZ9myZXWuDzFy5EhZw6qXViT248eP4/Tp0yK/ITH//5SecePGwcPDQ2n1MQyDSZMmIT4+HkOGDMHhw4frXKVIWhUVFZg1axYldaIwYWFhGDRokNwWvLGyssL169cxc+ZMTJw4EQkJCQgKChK7/qqqKowaNQrl5eWCbQzD4NGjRxg8eLDQNisrq3rX0T979iy8vLykezFEq6jEAl4SzbXXIoq+3a2yspLx9fVlADCLFy9mqqqqFNoekczu3bvZDkGtHDhwgDl37pzc6+Xz+UxwcDCjo6PDeHh4MCUlJTWOkeSzKu3n2tvbmykuLpaqrKLQ7W7ah253U2GlpaUYNmwYDhw4gAEDBiAoKEhuvWmGYbB7927ExcXJpT5tlZCQwHYIamXixIkYMmSI3OvlcDiYN28ezp8/j6tXr6J///61LvcpLkaKofh//vkHrVu3VvhjbwmRF0rsSpafn4/+/fsjKioKHh4e2Lx5s1zrZxgGhoaGcHR0lGu92mbbtm1sh6DW3r59ixcvXsitPnd3d0RFReHZs2fo2bMnMjIypKpHmglL27dvh5+fn1TtEcIGSuxKlJGRgZ49eyIpKQnnz5+Hjo6O3CfKcblcjBs3jq6nE1YVFxdj2bJlcr0f3dnZGbGxsSgtLUWPHj3w+PFjieuQtMdeUlKCjIwMuX9OCVEkSuxK8uTJE/To0QOlpaWIjY3FP//8I5eZvpWVlXR/LVE5VlZWCAkJkftzBj777DPcvHkTTZo0gaurK27evClReUl77IcOHZLbjHxClIUSuxIkJCTA1dUVZmZmuHnzJtq3b4+zZ89i6NChMtd9/vx5jX/EKNEM8npqnIWFBaKjo9GxY0f069dPose/+vv7S9SWvD6nhCgTJXYRpJlkU5u7d++iX79+sLW1RXR0NCwsLHDjxg24uLjIZQEab29vjB49Wg6Rkg/RrU3y5+fnh0uXLsmlrsaNG+PSpUvo27cvIiIicPHiRbHKSTKkLs/PKSHKRO9YEeRxP/mdO3fQv39/2Nvb4/LlyzAzMwMAnDt3DtOnT5eqToZhFLaONvkfRTwjWdv99ttvcHZ2llt9BgYGOHXqFD755BMMHToU586dk1vdgGyfU0LYRIldBFlXMYqLi4Obmxs6duyIS5cuCX1RCAwMRPPmzaWqd9asWYiKipIpNlI/Nzc3tkPQOLq6uoIvt/LSoEEDJCYmYvDgwRgxYoRUT28TRZbPKSFsosSuAPHx8XBzc8N//vMfhIeHy/VBLmvWrMHAgQPlVh8hbLl69apUM9s/pq+vj2PHjmHQoEEYPnw4Ll++LIfoCFFflNjl7MGDBxgwYADs7OyEkvqrV6/kct2+adOmMtdBiCro0KGDzMPn1RPnqpN7//79MXToUBrVIlqNErscpaSkYODAgWjTpg0uXryIRo0aCfZdvHgR69evl7jOiIgImVbaItI5c+YM2yFovBYtWmDJkiVSlz9y5Aj27Nkj+LlBgwY4efIkevXqhaFDh9LqgUQlnDp1Su4LkdWHEruc5OTkwN3dHcbGxggPD0fjxo2F9k+ZMgXz58+XqM6SkhKEhYXRUpYsCAkJYTsErSTJqNbIkSPxww8/CG0zMDDAn3/+iQ4dOmDQoEH0mFXCOnd3d+zdu1dud1qJgxK7HBQVFWHIkCEoLi7G5cuXYW5uXutxki7WYWRkhODgYDRo0EAeYRIJHDt2jO0QtM7jx48xa9Ys8Pl8sY7X19evdcEZY2NjnD9/HmZmZnBzc0N2dra8QyVEbEZGRnBzc8OpU6eU1iYldhlVVFRgxIgRSEpKQnh4ONq0aSNWucTERKV+gyNE1Tk4OGDatGl1rg6XmJgoVl3NmjXDpUuXUFZWhkGDBqGwsFBeYRINV1lZKfc658yZg61bt8q9XlEoscuAz+dj8uTJiI6OxtmzZ9G5c2exy0ZHR2Pnzp1C2yorK7Fo0SJaSY5ora5du4pM7OfOncPhw4fFruuTTz7BxYsXkZKSgmHDhgk9m51onvnz5yMnJ0emOo4ePYojR45IXG7lypW4f/++yP2tW7dGixYtEB8fL0t4YqPELoOlS5cK3gh9+vSRqOyMGTPwzTffCG0rLCxEnz59YGhoKMcoCVFPDMMIfckdPHgwVq9eLVEdHTt2RFhYGGJjY+Hr60ujZBqssLAQZWVlgp9jYmLg5OQEc3NzjBgxot7ykZGRiIuLw6RJkyRue/ny5fD390dqaqrIY+bPn49ff/1V4rqlQYldSkeOHMEvv/yCjRs3ivWmqc3HS1U2bdoUHh4e8giPyMjX15ftELReamoqRo0aJVhjnsvlSvXYVVdXVxw8eBAhISFS3ZlC1FPPnj0RGxuLgoICdOvWrc5j3717h2XLlmHdunVStdWgQQP89ttvmDhxosgvj927d0d6ejpev34tVRuSoMQuhYSEBEydOhWTJk2SeKa7KHfu3KHehAqhlefY17ZtW8ydOxe6uroy1zVq1CgsX74cS5culdt69UT1JSQkgM/no3fv3nUet2bNGnz99dcyTVS2tbWFtbV1nXfU+Pn5YcuWLVK3IS5K7BLKycmBt7c3OnbsiB07dkjVg6hWUVGBKVOmoLCwEAkJCTh+/LgcIyWyGDt2LNshaL2YmBjcuHFDbvWtXr0agwYNwpgxY/D8+XO51UtU1/Xr12FsbIyuXbuKPKa0tBS7d++Wy+N5582bh7Vr14rcP3LkSFy4cEHh8z0osUugsrISPj4+KC8vx6lTp2BgYCBTfVVVVfD19UWjRo0wa9Ys+Pj4yClSQtRfz5498fPPPwt+rqioELqGKikdHR0cOnQI5ubm8Pb2RlFRkTzCJCosOjq63if0hYWFoV27djXWHpGGs7MzXr58iSdPntS6X1dXF2PGjMGBAwdkbqsulNglsHDhQsTGxuLPP/+ElZWVzPUZGhrC1dVV8LMsvX9CNNGHn4kHDx5g2rRpMtXXuHFjnDlzBunp6Zg0aZLY98wT9cPn8xETEwMbGxv4+/tj0aJFGDhwYI3Z65GRkejRo0etdWzZskWQ9P38/ITeLzweDwsXLhQ6nsvlonv37nU+Rnj69OnYtWuXDK+sfrJfvNISe/fuxZYtW7B9+3b07NlT4e2Fh4dj4MCBlOxZEhMTo5TfMxF28eJFuLm51drDcnJyksvSnPb29jh06BCGDh2KNWvW1Fi9TtOVlgJiLgcgV3Z2gDJv+ElISEBRUREyMjJw5swZ6OjoYPfu3Rg2bBiSk5MF77GEhATMmDGjRvk5c+YgLCwMHh4eKCsrw59//gljY2MEBQUB+PfWuNomTjs4ONR565uZmRm6du2KiIgI9O/fX06vVhgldjHcuXMHM2fOxDfffFPrG0ASGzduRP/+/dGpU6c6j0tNTUVERAQGDBggU3tEOkFBQZTYlezx48eIiYmBu7u7yGOaNGkil7a8vLzw448/YsWKFfj888/h5eUll3rVQWIi4Oio/Hbj44EuXZTXXnR0NBo3bowTJ05AR0cHAGBtbY309HTEx8fDyckJAJCWllZjGP7atWt48+YNEhMT0bBhQwBAXl4eevXqhSVLlqBp06aIjY3F+PHja7RrZmaGmzdv1hkbwzDg8XjyeJm1osRej6ysLAwfPhxdu3bFli1bZOpBMwwDS0tLdOzYsd5j/fz8pG6HyO7o0aNsh6B1HBwchK6p16eqqkqmGfPff/897t+/jwkTJiAuLg52dnZS16VO7Oz+TbJstKtM165dQ8+ePYXmQmVkZAD49zkc1d69e1cjscfFxWHfvn1Cs+SbNWuGlStX4syZM2jbtq3I3naTJk3w7t07kXHl5+fj7t272L59u1SvSxyU2OvA5/MxZswYAMDJkydlXrOdw+Fg9OjR8giNKBgtEqT6AgIC4ODggGHDhklVnsvlYv/+/ejWrRuGDRuGhIQEQe9MkxkaKrfnzJabN29i2bJlQttu3boFAEJf4jgcTo25Fv7+/rXWOXDgQCxfvhwpKSlYs2ZNrcdwudw6e+O///57jcXJ5I0mz9Vh8+bNuH79Oo4cOYJWrVqxFgfDMDh8+DDd5040zrFjx6Rem3vJkiVijX7VxcTEBCdPnkRqaqrWXWvXZG/evEFBQQGcnZ0F2xiGwaVLl+Dq6oqWLVsKtjdu3FjsR2Obmpri1atXMDY2rrNtU1PTWvdVVVUhJCREqtXtJEGJXYRnz55h+fLlmDt3br2LG9SloKBA5lsbOByO4F53QjRFRkYGEhMTpR5O19PTg62trcxx2Nvb46effsLGjRvrvTZK1IOhoSG4XC4sLCwE20JDQ5GVlVWjp92mTRuxEzvw72S7UaNGidyfn58PGxubWvcdP34cHh4eMt8qXR9K7LXg8/mYMmUKLCwspF5isNqVK1fQoUMHmWOaNWsWHNmY8aKlFi9ezHYIGq9169ZYuXKlStz58d1338HZ2Rm+vr54//492+EQGTVs2BD9+/fH06dPAfw7V2rWrFlYu3YtXFxchI7t2bOnyPvOa9OpU6c6v1AmJSWhi4hrHVu3bsWcOXPEbktalNhrsXnzZsTExOCPP/6AkZGRTHX5+PjUueoRUU3W1tZsh0Ak8P79eyxZskTqy1U6OjrYt28f0tLSaEheQ+zatQtHjhzBwoULMXPmTPz222+1XjsfOHAgoqOjxaozLS2tzkmWDMMgJiYGffv2rbEvNjYWbdu2FRpFUBRK7B/5cAi+V69ebIdTKx6Ph23bttE1dwWaO3cu2yFopD179qC4uFju9TZs2BBffPGFTM9dt7OzoyF5DdK6dWuEhIRgw4YNOHv2LLy9vWs9rlevXsjOzhbr4SxhYWFwcHAQuT8hIQFNmzYV3Er3oU2bNmHBggXivwAZUGL/AI/Hg6+vr8xD8BkZGaioqJBjZMJ0dHSgp6eH5ORkhbVBiLy9efMGubm5Mo+CiTJmzBiRk5bERUPy2kdfXx+zZ89GcHBwvcdevnwZ3bt3F7l/27ZttSbvtLQ05ObmKm30lhL7B7Zs2YLY2FiZhuD5fD6mT5+Ot2/fyjk6YdOnT5fLxCFClKVp06ZYunSpSlxTF4WG5LXT4sWLceHChTrvP2cYBklJSWjfvn2t+9PT00WuYrd582aljgJSYv9/8hqC53K5OH36NMzNzeUYHVG2RDbW3CRyc/fuXalX9qIhee1jZGSEnTt31nl/+Zs3b0QO5/N4PMyePRv79++vcZdHcXExIiMjMXz4cLnGXBdK7JDfEHw1Rd/K8LGysjIEBATQNXc5ErVABZHMtm3bkJubq/R2nzx5ItNtpjQkr35MTU1lOvd++eWXmDp1KrZu3Vrr/mbNmiEgIKDWfWvXrsWCBQvw+eef19h38eJFTJ06VakjVbTyHP43BB8dHa2w63+KZGBggBYtWiA7O1to4QUiPVEfbiK+0tJSVFVVoVmzZkpvW9Ynt1UPyXfu3Bk//PAD1q9fL8foiCJs2rRJ5jrc3d3rfFaBKMuWLRO5HsPIkSNlDUtiWt9jl8cQfGVlJb799ltWe8y+vr6U1OWIbneTnaGhIebPn8/aNfW6nsEtDhqSJ+KS5ZkFiqDViV1eQ/DZ2dlwd3dX6UlBhBDJ0ZA8UUdandgPHjyI2NhY7NmzR6YheCsrKwwcOFCOkcnm3bt3+OGHH+iaO1G6DRs24MWLF2yHIeTcuXM4efKkVGWrh+RfvHiBDRs2yDkyQhRDaxN7WVkZVq5ciREjRsi0FrwqMjU1RYcOHVBUVMR2KGorMDCQ7RDUTlVVFczMzPDJJ5+wHYoQNzc3mUbT7OzsMGvWLPzyyy/Iy8uTY2SEKIbWJvbt27cjMzNT5KP3xJGTkyPHiORr7NixaNSoEdthqK3S0lK2Q1A7urq6mDJlispdktLX18eIESNkquO///0v+Hy+XO6aIUTRtDKxFxYWYs2aNfD19RW52EB9/vrrLyxdulTOkRFV8eOPP7IdAlEhzZs3x6JFi7Bt2zakp6ezHQ4hddLKxL5+/XqUlJRg1apVUtfh4OAgl9srlCErKwv+/v50zZ3IXVBQEP7++2+2wxBbSUmJ1JeovvvuOzRq1Eim8wYhyqB1iT07OxsbN27EvHnzYGlpKXU9+vr6ajPU3apVK/Ts2VOh69cT7cMwDNq1a4eOHTuyHYrY/vrrL3z//fdSlTUxMcEPP/yA/fv3S/SYT0KUjcNoWTdu7ty5OHToEJKTk9GkSRO2wyEqKi8vj5WFVYji5ebmonnz5lKVLS8vh52dHTp37ozTp0/LOTLJJCQkwNHREYcOHYK9vT2rsRDlePr0KSZMmID4+HiRz3wHADBaJDk5mdHT02PWrVsndR1nzpyRY0REVXl6erIdAlFRBw8eZAAwN2/eZDWOtLQ0xtDQkAFAf7Toj6GhIZOWllbne0OreuwTJkxAVFQUnj9/DkNDQ4nLJycnY8+ePVi7dq0ColOepKQkbN++HRs3blS5GcyqIiEhoe5vxFoqMDAQ3bp107hbRCXB4/HwxRdfwMzMDNeuXWP1M5Senk634GmZZs2a1bsyptYk9gcPHuCLL77A9u3ba32snra5evUqevfuLfOym0S7REVF4auvvtKIL4R37tyBnZ2dVM9wP3/+PDw8PHDhwgUMGjRIAdERIj2tSeyDBw/G8+fP8fjxY+jp6bEdDiGEZVeuXMHTp08xb948icsyDIPevXujsLAQCQkJ9AWZqBStSOzR0dHo06cPjh07Bh8fH7bDUUkMw2hEL4zInya/N2R5bTdv3oSLiwsOHz6McePGyTkyQqSn8V8zGYbB0qVL4ejoKPXj83bt2oXCwkI5R6Y67t69iwULFtB97h/Ys2cP2yGohKCgIJw5c4btMBRGli8sPXr0gJeXF3744Qe6lZSoFI1P7OHh4bh9+zYCAgKkGi7j8/lIS0tTm3vWpeHk5ITJkydrbK9MGgkJCWyHoBIGDBgAb29vtsNQWWvXrkVqair27t3LdiiECGj8UPygQYOQl5eHu3fvsh0KIURFHTx4EBMnTpSq7PDhw/Hs2TP8/fff9OWYqASN7rEnJyfj4sWLmD17NtuhqBUej0fD8lqsqqqK7RCU7tmzZ8jKypKqrJ+fHx49eoSYmBg5R0WIdDS6x7548WLs2bMHmZmZaNiwIdvhqI2IiAicP38ev/76K9uhECXbsGEDmjZtismTJ7Mditrg8/mwt7dHly5dEBISwnY4hGhuYn///j2srKzg6+uL9evXS1z+2bNniIuLw/jx4xUQnepLSUlB27Zt2Q6DKFlKSgratGlDQ8oS2rRpE/z9/ZGeno6WLVuyHQ7Rcho7FH/8+HHk5+dj5syZUpV/8uSJVq88pu1J3cvLi+0QWNG2bVtK6lKYNGkSdHV16W4KohI0tsf+5ZdfwszMDBcvXmQ7FLVXVlaGBg0aaNUJ//Lly3Bzc2M7DKV4//49Xar6f3fv3oWBgYFUT6ybNm0aLl++jJSUFOjq6iogOkLEo5E99nv37iEuLg5+fn5sh6IRwsPDsWzZMrbDUCptSepbtmzB7t272Q5DZTRv3hwXLlyQqqyfnx8yMjJw/vx5OUdFiGQ0ssc+depUREREICUlBTo6OmyHoxFycnJgbm7OdhhEznJyctC8eXOtGo1RpG7dusHU1BSXLl1iOxSixTSux15QUIAjR45gxowZUiX1ffv2SX3biyajpK6ZzM3NKanLkZ+fHy5fvoxnz56xHQrRYhqX2Pft2wcej4epU6dKVT4tLQ0tWrSQc1Sa5e3btxp/n7smL6NaUFDAdggay8fHB02bNsWOHTvYDoVoMY1K7Hw+H9u3b8eoUaOkTs4rV66kJzXV4/z58/jxxx/ZDkOhNPV+5N27d2Pnzp1sh6Hy3r59i4iICInLGRgYYOrUqdi7dy9KS0sVEBkh9dOoa+xXrlyBm5sbYmJi4OLiwnY4Gq2oqAgmJiZsh0EkVFRUBGNjYxp+r0dVVRWmTJmCAwcOSFw2JSUFtra22LNnD3x9fRUQHSF106jEPmzYMKSkpOD+/ft04iKEsGbIkCHIycmhZ1QQVmjMmHNWVhZCQ0Mxa9YsqZL64cOHUVlZqYDINF9mZqbGX3NXZ5mZmWyHoHX8/Pxw7949ekogYYXGJPawsDBwOBz4+PhIXJZhGNy4cQN6enoKiEzzXbp0Saple4nihYSE0GpoLHB3d4eZmZlGT8IkqktjhuI9PDxQXFyMa9eusR2KVqqoqIC+vj7bYciNr6+vRjxju6KiAnp6enRpSkoVFRV48uQJOnfuLHHZCRMm4NGjR7h//74CIiNENI3osZeUlCAiIkJr1/dWBZqU1AHNWXlOX1+fkroMdHR0sHTpUqnKenl54cGDB0hLS5NzVITUTSMS+5UrV1BeXg5PT0+2QyEAEhMT1f6a+9ixY9kOQWqJiYlsh6AxdHR0pB5Od3d3h56eHsLCwuQcFSF104jEHhoaCnt7e3z66acSl01ISEB5ebkCotJe0dHR2LVrF9thaKXz58/j8OHDbIehUQwMDKQqZ2pqij59+iA0NFTOERFSN7W/xs7j8dCqVSv4+voiMDBQ4vJDhgxBaGgorSkvZ3w+nxb6YQGfzweHw6HhdxWxZcsWLFy4EHl5eWjUqBHb4RAtofZn3ri4OOTm5kp9ff3UqVOU1BVA3ZN6TEwM2yFIhcvlUlJXAIZhUFxcLHE5T09PVFZW0kNhiFKp99kX/w7DN2vWDN26dZOqfIMGDeQcEfnY7du31e6ae1BQENshiO3WrVtsh6DxMjIysGDBAonL2djYoFOnTjQcT5RKIxK7h4cH9bpV2F9//YUTJ06wHYZEjh49ynYIYomNjcW5c+fYDkPjWVtbY/bs2VKV9fLywvnz51FVVSXnqAipnVpfY3/+/Dk+/fRTnDp1CsOGDZOobHl5OfT09NR+yFhdMAxDQ8QKQv+3qu3u3btwdnbGtWvX0Lt3b7bDIVpArbNaWFgY9PX1MWDAAInLbtmyBVFRUQqIitSGEo/i0P+tanN0dETLli1pOJ4ojVon9tDQUPTr1w/GxsYSl+3bty9cXV0VEBWpT3h4uNpdc1cl4eHh4PP5bIdBxMTlcuHp6YnQ0FB63xOlUNvEXlBQgBs3bkg9G75Lly40cY4lqampiIyMZDuMOi1evJjtEGr1+PFj3Lx5k3rpLPnjjz/w6NEjict5eXnh+fPn+OeffxQQFSHCdNkOQFrh4eHg8Xjw8PBgOxQiIT8/P7ZDqJe1tTXbIdTKwcEBP/30E9thaK3OnTujqKhI4nL9+vVDw4YNERoaCjs7OwVERsj/qO3kuW+++Qa3b9/Gw4cP2Q6FEELqNXjwYDAMg/DwcLZDIRpObYfi4+Pj4eTkJHE5hmGwcuVKBUREpMEwDA4fPkzXHutw7NgxVFRUsB0GkVHXrl0RHx9P73WicGqZ2MvKyvDw4UM4OjpKXPbdu3do1aqVAqIi0uBwOCgsLERCQgLboaikjIwMJCYmQk9Pj+1QiIwcHR2Rm5uLjIwMtkMhGk4th+Kr7wu9ffs2vvzyS7bDIRooMTGRroWSWpWVleHmzZvo27evROUyMzNhZWUl1bobhEhCLXvs8fHx0NHRQadOndgOhWgof39/tkMgKkpfXx+//fabxOUsLCzQokULxMfHKyAqQv5HbRO7g4MDGjZsyHYoRM54PB62bt3K+nXIrVu3stb2nj17pHrgCFEOLpcr1RLJHA4Hjo6OlNiJwqltYpfm+vqbN2+QlJSkgIiIvOjo6EBfXx/JycmsxsHW7W75+fnIzc2FkZERK+0T8Ui7jkB1Ymf7iyvRbGqX2MvLy/Ho0SOpEvvFixdx9+5dBURF5Gn69OmwtbVlOwxWNGnSBEuXLqUFaDRU9QS6ly9fsh0K0WBqt0DNw4cPUVlZKVViHz16NC3FSQiRCx6PJ/FTJavPW2/bxJUAACAASURBVPHx8WjdurUiwiJE/Xrs1RPnPv/8c4nL6urqQl9fXwFREUUpKytDQECA0ocuAwMDldbW1q1bkZubq7T2iHxIM7Pd0tKSJtARhVO7xH7v3j2aOKdFDAwM0KJFC+Tk5Ci13dLSUqW1w+fz0axZM6W0R+RnwYIF4PF4EpWpnkB37949BUVFiBrex96lSxd07twZf/zxB9uhEEKIxFasWIEdO3YgOzub5lIQhVCrHrssE+dCQkJw5coVBURFCCHiowl0RNHUKrHLMnGuVatWcHBwUEBURJnevn2LFStWqPXtQhs3bkRqairbYRCWfDiBjhBFUKvELsvEuT59+sDCwkIBURFlaty4MTp06KDwBVzy8vIUUm9VVRUaN24MGxsbhdRPlGv//v0Sl6EJdETR1CqxJyUloW3btjRxTsuNGTMGJiYmCm1jypQpCqlXV1cXU6ZMoWurGuL27dsS30LL4XDg4OBAi2URhVGrxP7y5Uu695MoxapVq9gOgaiB7du3g8uV/DRqZWVF19iJwqhdYre0tJS4XGZmJh49eqSAiAjbsrKysHjxYrlfc+/SpYvc6goMDMSDBw/kVh9Rf5aWlpTYicKoVWKvfuyhpG7evEknVg3VqlUr9OrVC5WVlWyHUiuGYWBra0tPIiRCrKys8OrVK1oJkyiE2iwpy+fzpU7so0aNUutZ1KRunp6ebIcgEofDwYgRI9gOgyhQRUWFxCtaWllZoaqqCjk5OWjZsqWCIiPaSm167Lm5uaiqqpJqKB6Q/mlMRDvt2bOH7RCIGqiqqoKPj4/E5arPY5mZmfIOiRD1SezV16Ok6bET7ZGUlIQFCxbIPEKTkJAgddmAgABcu3ZNpvaJetDV1cV3330ncbnq8xhdZyeKoDaJvfqbrbQ9dqIdPvvsM3h7e8uc2Ldt2yZ12S+//BK9e/eWqX2iPnr16iVxmebNm0NPT4967EQh1Caxv3z5Erq6ujA3N5e47NSpUxUQEVFVffr0keoWJHn56quv6NIPqROXy4WFhQX12IlCqE1iz8zMhKWlpcQnbD6fjwEDBigoKqLqGIZRysRJmpxJJGVlZUU9dqIQapPYpb2HncvlYsyYMQqIiKiDu3fvyuWae12CgoJw5swZhdVPVNutW7eQnJwscTm6l50oitrc7paVlUVrvROJOTs7Q19fX+KhcS8vL4SGhop17IABA9C5c2dpwiMaICMjA4WFhWjXrp1E5SwsLPDw4UMFRUW0mUr22P39/ZGTkyO0rbCwEKampixFRNSZNEl3zpw5Yh/7xRdf0DV1Lebj4wN3d3eJy5mamqKwsFBucdR23iTaSSUTu7e3N37//XehbUVFRTA2Npa4rufPn+PVq1fyCo2oOR6PJ9awvJubW537q6qq5BUS0VLGxsYoKiqSW321nTeJdlLJxN6jRw/cuXNHaLnF4uJiqZ7odeHCBTx58kSe4RE1FhUVhYULF8pUx4YNG3Dw4EE5RUS0lYmJCYqLi+U2/6O28ybRTip7jX3o0KE4ffq0YDnOoqIiqRL7rFmzaJiUCAwYMEDia6EfGzZsGNq0aSOniIi2MjExAZ/Px/v372FoaCiXOj8+bxLtpJI9dgAYP348Dh06BODfW4mkTex6enrQ1VXZ7y+EBW3btq33mLpmubdt25a+LBKB4uJiTJo0SeJy1eczeQ7Hf3jeJNpLKYl9wYIFNbatW7cOixYtwqpVqzBp0qQab25DQ0PY2NggMTERFRUVqKqqkuoaOyF1KSsrq3UoNCQkROjn9+/fKyskoobc3NxQWloqUZnq81lxcbHIYz4+d0py3iTaSymJ/eOZn9u2bcP169exfv16rFq1Cvb29pg4cWKNcjNnzsS2bdsEb15peuyE1CU8PBzLli2rsf3YsWOCf2/ZsgW7d+9WZlhEDdy6dQvz5y1AfxcvbPxpD/p298D8eQtw69YtscqL02P/8Nwp6XmTaC9WhuKDgoKEhq6+/vprhIaG4vnz50LHtW/fHq9evUJ+fj4AwMDAQOK2vv/+e5SUlMgWMNFYw4YNq/chHqNHj5bo9jei+fbv34+5075H9Mk3MC8bBDu9MTAvG4Tok28wd9r3OHDgQL11NGzYEEDdo0EfjiZJet6k8572Unpif/bsGTIyMtChQwfBNgsLC5iamuLq1as1jp84cSJOnDgBANDR0ZG4PRsbG+jp6UkfMNF49T1/wNzcnK6pE4Fbt25hS9ABmJR0g5etL7q0csKnTT9Dl1ZO8LL1hUlJN2wO3F9vz716eey6ZsVXv++SkpIkPm+K8+WCaCalJ/bk5GRwOBw0atRIaLuJiQnS09NrHO/l5YWIiAgAkOrBHtOmTYO+vr50wRKt8/btWzAMg4KCArZDISrqaMgxVBVYwNW6n+CclPTm3yTO5XLhat0PVQUWOBpytM56qsuKc3taSkqKxOfNsLAwsV4P0TxKny5efcI0MjIS2m5sbFzrybT6KUjV/yZEkc6dO4ddu3YhM/0NVi87D9s2FUL7k5L10awJD03MeIJtb99x8TpHD3aflgsdm5qmByNDBubN/7eYTUkpBxmZ+mhnU44PB5IyMnXB5QKWrf53bHk5kJreAJ9YVaBhw//16rKydVFRwcEnrSsF2/h8ICm5ASxbVsLE5H+JIi9fB2/f6dDrkNPrSErm4MmN92jfvAsqOMUAA7wrM8CdV+dh27QruNADl8uFtUkn3IkOR2lpqchb2arPZzwer9b9H5LmvGljY4Pk5GSZb+8kaohRAl9fX8G/jx07xnC5XObNmzdCx9ja2jIzZsyoUZbH4zGurq4MACYqKkpo3+TJk5kjR44Ibbtx4wbj6enJlJSUCG1ftGgRs3nzZqFtT58+ZTw9PZm0tDSh7QEBAcyKFSuEtuXm5jKenp5MfHy80Pbdu3czfn5+NeL29PRkLl26JLTt9OnTjI+PT41j6XWozuvYs2cPY96sJQOYM8BkBmA++uPDAKc/2naJATxrOdaPAXZ/tC3+/4/N/Wj7CgYI+Ghb2v8f+/Sj7ZsZYNFH20r+/9gbH20/Qq9DKa/Dm1nS6yyzsvdVZmXvq4xPhy2MqXFT5syZM0LvryNHjjCTJ09mGIZhkpKSGABMdHR0jfdrtepzpzTnTXd3d5H1Es3GYRjJlj06fvw4Tp8+LfKaI8Mw4HA4GDduHDw8PAAAU6ZMwR9//AEAuHr1Kvr374/s7Gw0a9ZMUM7CwgITJ05EYGCgUH2nT5/Go0ePsGLFCkRERKBfv36ShIunT5+iffv21NsnYikpKQFTCXh5jse0icGs9xA1paerKa8jKZmDo/t+QRO+Hdo0/rcn/K7MAFee/4xxHX8AF/9WkpB1FzkG4Yi6dU5kj/2ff/6BnZ0dbty4gZ49e9Z6TPW5U5rzZlZWFvz8/Gqtl2g2iYfifXx84OPjI3WD1St2ffgGZRgGb9++rXXhkAMHDmDdunVYsWKFVEsl/vjjj/jjjz/ktrIT0WzVQ51RN2pfoMZ5gPh1Of9fe3ceF1W5/wH8AwIqgpqYZoCpaaIgFVLuu6ImIDc1d8srKuAtres1xRYrtTS1xD0NzDD3hS0QRU1RQ8GrggvushqKgGwKM3N+f3jhJ6nInDkzZ5bP+/XqVQ3nec5HX8x853nOc56jxnmfdWwPNfrorM75+OcQdWwPAOeu1cUfO0+jbYPXYW5ujjp1gXEdvq48RqVSIa3wHHoN7FDt507F51lNBh1iPje5UY3p0vkwtkWLFmjdujVSU1MrX7t06RIePnyIvn37Vjk2NTUVjo6OlRs51ORa1N/98MMPom6TI9Nx69atan+elpam1ee5k2EZNXokLF7IwtG0uCcGGyqVCkfT4mDxQhZGjR5VbT8Vbau746Li907M5+bfr8eT6ZBlfnrChAlVbsXYuHEjvL290aZNmyrHrVmzBgEBAZWFWczuX82aNeM0PD3Tjh07EBISUu0xsbGx+PHHH3WUiPRdly5d8NGn76Ow3p8IvxqC09mncCX3Mk5nn0L41RAU1vsTH336Prp06VJtPxU71VXcz/40jxd9dT83yXTJson6p59+ijlz5mD69Olo0KABbt++jY0bN1Y5pri4GOnp6XBycsLDh4+ulVW39SKRGD4+Phg+fHi1x/j6+qK8vLzaY8i0TJgwAW3atMHWLVuR8Ec0MssAyzpAr4EdMGp0wHOLOvD/n2c13VFT3c9NMl2yFHYLCwt8//331R4TGhqKcePGAQBq164NS0tLSR+WQATgmZsXjRw5ssq2stzkiP6uS5cu6NKlC27fvo3PPvsMQUFBaq3lUXerbHU/N8l06e0cdVhYGIYOHVr5/7a2tqIK+65du3Dx4kUpo5GBS05Ofu4xo0ePfubPUlJSeM2dKtnY2MDb21vtBbraeAbG3z83yTTppLCr+yF49OhRdOvWrcq1cRsbG1GF3cLCAmVlZc8/kEzCvn37qozEn8XHx+eZP4uPj3/udXkyHRWFXV2FhYWPVtVXs7hXnc/Op31ukmnSyVR8gwYN1Do+MjISM2fOrPKara2tqGvs/PZKj/Pw8ICHh4dGffj5+XHEThorKiqCra1ttavi1fnsfNrnJpkmtTeokUuXLl3Qvn17/Pzzz3JHISLS2Jdffong4GCkp6fLHYWMjMHM2dSvXx8FBQVyxyADdOTIEbVH2LGxsTU+9ujRoxzBm7ArV64gOztb7XYFBQVPPNSFSAoGU9hffvllZGVlqd1OqVSKetORcTh58iT27dundruVK1fW+Njk5GTs3fv0nerI+O3evRvXrl1Tu11WVlblA66IpGQwU/GfffYZNm3a9NRHFFanpKQEEydOrNGCKSIidZWXl8PMzAwWFuotWeratStee+21J+5FJ9KUwYzYHRwckJ2drfa2stbW1vjiiy+0lIqITJ2lpaXaRR0AMjMz4eDgoIVEZOoMprDb29tDoVAgJydH7bbOzs5aSET6KiIiQtRzBaQSFhbGa+5ULaVSiaysLNjb28sdhYyQwRT2im+2GRkZMichfXb58mWcOnVK1nt5MzMzceTIEdnOT/ovJycHCoWCI3bSCoMp7BXfbDMzM2VOQvrstddew9dff13tvcE1MW3aNNFtAwIC0KtXL43OT4ahvLwcH3/8sdrtKj7HOGInbTCYwt64cWNYWVmJGrHHxsYiJSVFC6nIWLm5uckdgQzAgwcP0KlTJ7XbVXyOccRO2mAwhd3c3Bwvv/yyqBG7IAi4e/euFlKRPti8eXPlEwClMmnSJEn6EQQBISEhvOZupGxtbTFqVPXPXX+azMxMWFpaonHjxlpIRaZOlqe7ieXg4CBqxD5w4EAtpCF9kJ2djevXr8PKykruKE9lZmaGhw8fIjk5Ga6urnLHIT2RkZEBe3t77utOWmEw97EDj564dfv2bRw6dEjuKEREoo0fPx43b97E0aNH5Y5CRsigvi7a29tzVTzpxOnTp+WOQAbgxIkTotpVjNiJtMGgCruTkxOuX7+O4uJitdvm5OTIem8zSeenn37C/fv3tXqOefPmaaVfhUKB5cuX85q7kViwYIHabQRBQEpKCpycnLSQiMjACnvHjh2hUqlw9uxZtdsuWrQIV65c0UIq0qX8/HwUFBTA1tZWq+cJDg7WSr8WFhawtrbGrVu3tNI/6db27dvVbpOeno67d++iY8eOWkhEZGDX2MvKymBra4vvv/8eH330kVpt09LS0LBhQz5NiYhktXv3bgwbNgyZmZl8CAxphUGtireysoKrqyuSkpLUbtu8eXMtJCIiUk9SUhJeeuklFnXSGoOaigceTceLKexkuIKCgnD79m25Y2hFSUkJFixYwGvuJiQpKYnT8KRVBlnYL168KGoBHRmeBw8eoFatWmjatKlOz/vll1/q5DzW1tZwcHBAbm6uTs5H0pk8ebLabQRBYGEnrTPIwi52AV1oaChu3rwpfSjSmjp16mDatGka7/2uLmtra52d6/333+cOZAZGEAT07NlT7XZcOEe6YHCF3cXFBVZWVkhMTFS7bZMmTUQ99pVMz6effip3BNJjZmZmGD9+vNrtKj633N3dpY5EVMngCrsmC+g8PDzw9ttvayEVSWnJkiW4evWq3DFkce/ePQQGBvKau5HiwjnSBYMr7AAX0BkzpVKJpk2b4tVXX5U7iiwaNWqEN998EyUlJXJHIS3g9XXSBYMt7FxAZ5xq1aqF8ePH6/ya+t+lpaXJdu4RI0agXr16sp2fqqdUKhEREaF2Oy6cI10x2MIudgHdvXv3cOPGDS2kImPyr3/9S+4IpKeuXLkiao0PF86RrhhkYa9YQCdmOj43NxdLly7VQioSa9GiRXp3aWXx4sVyRwDwqBjMnDmT19z1iJOTk6hnCVT8jrOwk7YZZGG3srJChw4dRH1rbt26NRYuXKiFVCSGIAho164d3Nzc5I5Shb48oMPR0RF9+/aFQqGQOwo9RsylosTERDRt2pQL50jrDGqv+Mf5+fnhyJEjuHDhgtxRiIiey8PDA5aWloiKipI7Chk5gxyxA0Dfvn1x8eJFPiWLiHSmqKgIKpVK7XbFxcU4cuQI+vXrp4VURFUZbGEfOHAgLC0tRa1OBcBrljJatGgR9u/fL3eMaq1YsULuCE91/vx5TJ8+nb+/MgkMDMTly5fVbrd//348fPgQXl5eWkhFVJXBFvYGDRqgd+/eCA8PF9V+woQJePDggcSpqCa6du2K/v37yx2jWnLe7lYdZ2dnjBgxQu4YJuuDDz5A27Zt1W4XHh6Odu3aoU2bNlpIRVSVwV5jB4CVK1fik08+wZ07d9CgQQO12sbHx8PZ2RkvvPCCltIRET26771Zs2b45z//ie+++07uOGQCDHbEDgBeXl4oLy/Hvn371G7bvXt3FnUdMuDvj3pNEAT+3eq5hIQE3Llzh9PwpDMGXdhfeeUVuLq6ip6OJ91YvHgxduzYIXcMo3TixAnMmDFD7hhUjfDwcDRu3BidO3eWOwqZCAu5A2jK29sbq1atgkKhgIWFwf9xjNI777wDZ2dnuWOopaSkRKePbhWra9euqF+/vtwxjN6VK1ewb98+UTsSRkREwNPTE7Vq1dJCMqInGfSIHXhU2PPy8nDs2DG125aWlurt6mdj4uLiIvve7+oaNWqU3BFqzMXFRe4IRi8/P1/UiPvq1au4cOECvL29tZCK6OkMvrB37NgRzZo1EzUdX7duXdy5c0cLqai8vFzuCBqZNWuW3BFEUSgUvOauBW+99ZaoZ6hHRESgdu3aGDBggBZSET2dQa+KrzB16lTExcXhypUrBjcyNEbLli1D/fr14evrK3cUkxMdHY0DBw7weQh6ok+fPrC2tuZuc6RTRlHYo6Ki4OnpiQsXLqBdu3ZyxzF5aWlpcHR05JcsmaSlpaF58+ZyxzB59+7dQ5MmTbBq1SpMnTpV7jhkQgx+Kh54tL2stbU1V8friebNm7Ooy4hFXToKhQIbN24U1TY6OhpKpRKenp7ShiJ6DqMo7HXr1oWHh4fo7WXz8vIQHx8vcSrTUlxcLHcESW3ZskXuCJIoKSnhNXcNXLhwAWVlZaLaRkREwN3dHfb29hKnIqqeURR24NFmNcePHxe1GM7a2hpr167VQirTsHr1aqxfv17uGJKKjY2VO4IkoqKiMHfuXLljGCxXV1dMmTJF7XZlZWWIjo7mpjQkC6O4xg4AOTk5sLe3x9KlS/HRRx+p3V4QBE4fi5Sbm4tGjRrx709P5ebmws7OTu4YJmXPnj149913ce7cOXTo0EHuOGRijKawA8DIkSNx7tw5XLhwgUWGiGTTv39/lJaWitpfg0hTRjMVDwABAQG4dOkSDh06JHcUo3f37l25I5AIubm5vOZeA+Xl5Th48KCotpcuXUJcXBwCAgIkTkVUM0ZV2Hv27In27dtj9erVotqXl5cjOTlZ4lTGJyQkBD/99JPcMUiEqKgoLFiwQO4Yeu/QoUO4ePGiqLZr165F48aNMXz4cIlTEdWMUU3FA8CqVaswffp03Lp1S+3VqEqlEu+88w5iYmI4lV+NkpIS1K1b16j/jkaOHIlt27bJHUMrDGUffLmpVCqYm6s39ikuLoa9vT38/f3x7bffaikZUfWMasQOAOPHj0edOnVErdKuVasW9u7da9QFSwrW1tZG/3c0evRouSNoDYt6zahb1IFHt0nev3+fG9KQrIxuxA4A/v7+CAsLw61bt2BpaSl3HKNw69YtvPLKK3LHIIndunWLGwpJRBAEuLm5wcHBQfSeGkRSMLoRO/CosGdnZyMsLEzuKEZhx44dCAkJkTsGacH+/fvx448/yh1Db2RkZCA9PV1U24SEBJw5c4aL5kh2RjliB4AePXrA0tJSo5WtTk5OEqcyTAqFArVq1eKozkgpFApYWFjIHUMvfPzxx5g0aZKoR+FOmDAB8fHxuHr1qqhpfCKpGO1vX0BAgEYrW4OCgpCSkiJxKsNkYWFhckXdWHaeqwkW9f+3ePFiUUX97t272LZtG/z9/VnUSXZG+xv47rvvokmTJlizZo2o9osWLUL79u0lTmU4TP22v5UrV8odQRbJyckmfZ+72DU5wcHBMDMzw8SJEyVORKQ+oy3stWvXhq+vL3755RcUFRWp3d7W1tZkv3nHxsYa7a1eNWWqTwo8duyY6KeZmSqlUom1a9di5MiRaNy4sdxxiIz3GjvwaMVvq1atsGbNGlEPcjBVFb8Spjb9To+Y4nMTjh49iu7du4v6c//+++8YMmQI/vzzT3Tq1EkL6YjUY9SFHQCGDh2Kmzdv4syZM6LetAUFBbh37x5atmyphXREJLfc3Fx8+OGH+O2330S19/T0RHZ2NhITE03uCxHpJ6Ofa/7www9x7tw5REVFiWpfWlqK2bNnS5xK/xw5csSkr63S05nC74WdnR1+/fVXUW1Pnz6NqKgofPjhhyzqpDeMvrD369cPvXv3xpw5c6BUKtVu/9JLL+GXX37RQjL9cerUKezbt0/uGHpl2rRpckfQCykpKSaxH0StWrVEtQsMDETbtm0xbtw4iRMRiWf0U/EA8Oeff6JLly7YtGkTxo8fL3ccMgA///wzJk2aJHcM0mOHDh1C3759sXPnTgwbNkzuOESVTKKwA49ufzt9+jRSU1NRu3ZtueMQkcyOHz+O5s2bw8HBQe22giCgc+fOEAQBCQkJnIYnvWL0U/EVFixYgPT0dKxbt050H0eOHEFeXp6EqeQTHh4u6tIEmbawsDCjuea+adMmNGzYUFTbPXv24OTJk/juu+9Y1EnvmExhb9euHT744APMnz8fhYWFovsJDQ2VMJU8Ll++jMTERJO9T5/Ey8zMxJEjR+SOIYm1a9fCxsZG7XYKhQKBgYHw8PBA3759tZCMSDMmMxUPAOnp6WjTpg1mz56NefPmyR2H9Njp06fh5uYmdwzSQxs2bMDkyZORlJTE3xHSSyZV2AFg5syZWLduHa5du4YmTZrIHYf0lLe3t8nuPkfPVlpaijZt2qB79+7YunWr3HGInsrk5mLnzJkDc3NzLFiwQO4oOrV582Y8fPhQ7hgGIzg4WO4Iek8QBISEhBjUNffY2FjRT3wEHj1D4K+//sL8+fMlTEUkLZMr7HZ2dpg1axbWrFmDGzduiO5nxYoVyM7OljCZ9mRnZ+P69euwsrKSO4rB4J7fz2dmZoaHDx8a1FMQb9y4IXrb1/z8fHz77bfw9fVF69atJU5GJB2Tm4oHgOLiYrRu3RoDBgzApk2bRPWRnJyM7OxseHh4SJyOiPRRYGAgli9fjqtXr6JZs2ZyxyF6JpMs7ACwZs0aTJs2DWfOnIGrq6vccYhIj2VlZaF169b4+OOPTe4yHhkek5uKr+Dr64tWrVohMDBQ7ihasW7dOhQUFMgdw2B9+eWXckcwOAqFAj/++KPeXXN/+PChxns2fP3116hTpw7+85//SJSKSHtMtrBbWlpi/vz5iIqK0nif9OLiYr36MCsoKMD9+/dRv359uaMYLGtra7kjGBwLCwvUq1cPaWlpckepYvbs2Th+/Ljo9mfPnsWGDRsQGBgoekMbIl0y2al44NGqXg8PD1y6dAkpKSlo0KCBqH6WL1+Ohg0b4v3335c4IRFp6urVq6IXu5WXl+Ptt9+GUqlEYmIiF6CSQTDpwg4At27dgouLC0aNGoX169eL6kOpVCIrKwuOjo4SpyMiOX311Vf45ptvkJCQgI4dO8odh6hGTHYqvsIrr7yCJUuWYMOGDaKn5GvVqiV7UQ8KCsLt27dlzUD0uJKSEsyfP1+vLlOp4+zZs5g/fz7mzJnDok4GxeQLOwBMmTIF/fv3h6+vr0EuOHvw4AEsLCzQtGlTuaMYDX27TmyIrK2t0bx5c+Tm5ur83Lt27cK9e/dEty8vL8cHH3yAdu3a4fPPP5cwGZH2sbDj0UYbGzZsQH5+PmbOnKlRXxcvXsT+/fslSlYzderUQUBAAJ8yJaF//etfckcwChMmTND5Zj/l5eU4duyYRgvdFi5ciOTkZISEhPC6OhkcFvb/kWJKHgBatmyJo0ePSpiM5LB48WK5I5BIlpaWWLZsmeinF3IKngydyS+ee5xUq+R1YenSpfD29kabNm3kjkJUI7m5uVi2bBnmz5+vt7NLXAVPxoAj9sdIOSWvTUqlEk2aNOF+1WRQ7Ozs8MYbb6CkpEQr/WtyTb1CxRT8xo0bWdTJYHHE/hTr1q2Dn58fYmJiMHDgQI36Sk9Pl33FPJGx279/PyIjI7F8+XLRfZw9exbu7u6YPXs2vvnmGwnTEekWC/tTSDklP2bMGAQGBsLFxUXChKRtK1aswIcffih3DKqh4uJiWFhYoHbt2qLacwqejAmn4p+iYkq+oKBA4yn54OBgODs7a5xp0aJFSExM1Lgfqhne7qZ96enp+Pe//y3Jfe716tUTXdQBTsGTcWFhf4bHV8nHxMSI7qdOnToaLxQSBAHt27fnhIG97wAAF39JREFUCl0d+v777+WOYPQcHR3Rv39/KBQKUe2lmmw8c+YM5s+fj8DAQLi5uUnSJ5GcOBVfDUEQMHjwYCQlJSEpKQnNmzfXuE+lUolatWpJkI7IdKlUKkyaNAnffvstXnrpJdH95OXl4a233oKNjQ1OnjzJ0ToZBY7Yq2FmZobQ0FDY2NjAx8dH49W858+fx6RJkwx2i00ifaFSqfDPf/5To6KuVCoxatQo5OXlYffu3SzqZDRY2J+jcePG2Lt3L1JTUzF58mSNirKzszNmzZpVo6n57777DrGxsaLPRZrR1i1Z9Gznz5/H9OnTa/Qes7CwQI8ePTQ6X2BgIA4cOIBt27ahVatWGvVFpE9Y2Gvg9ddfR0hICH777TcsW7ZMo77at29fo+O6d++OAQMGaHQuEm/UqFFyRzA5zs7OeO+993Ryrq1bt2Lx4sVYsmQJ+vfvr5NzEukKr7GrYc6cOVi8eDFiYmIkKbqCIOjtDlymLj4+Ht27d5c7Bj1m7969MDMzw9ChQzXq58yZM+jatSuGDRuGTZs28T1IRoeFXQ1KpRKenp5ISEhAYmKixtN3GzZsQN26dTF27FgALPREj6v4aKp4T+zcuRNDhw6FpaWl6D7v3r0Ld3d32NnZIT4+HnXr1pUkK5E+YWFXU15eHt5++23UqVMHJ06cgI2Njei+KjbD6NSpE77//ns0b94cI0eOlDAtkeE6duwYtm/frtFuco8rLy/HwIEDkZKSgsTEREnuciHSRyzsIly4cAGdOnXCwIEDsWPHDklG2SkpKXB2duaInegx58+fl2SDJwCYMWMGVq1ahbi4OPTs2VOSPon0ERfPidC+fXv8+uuv2LVrFxYsWCBJny4uLrwNTo9s2bJF7ggmLy4uDvHx8ZL0tXHjRixfvhzLly9nUSejx8Iuko+PD7766it8/vnn+OWXX0T1UV5eXuX/ly5dil9//VWKeKQh3mooP5VKhQkTJlT+f3l5uagvv/v27cPkyZMxefJk+Pv7SxmRSC9xKl4DgiBg6tSpCA4ORlhYGIYMGVLjtj/88ANsbGwwefLkytdUKhWuX7/Ox7ESPUV0dDTi4uKwZMmSGrc5efIk+vbtiz59+mDPnj2wsLDQYkIi/cDCriGFQoHhw4cjNjYWBw8eROfOnWvULi0tDY6OjrymTvSY5225rM5jkFNTU9G9e3e0adMGBw4cgLW1tVQxifQaC7sESktL4eHhgQsXLiA+Ph7t2rWTpN+cnBzY2dlxb3kyCUuXLkXDhg0xadIkjfvKyspC165dYW1tjfj4eDRq1EiChESGgYVdInl5eejZsycKCgpw/PhxODg4PHFMcXEx6tWrV+M+w8PDcfjwYY13uyMyBLdu3ULz5s1rPItVXFwMa2vrJ47Pz89Hz549kZeXh+PHj9d4hE9kLFjYJZSZmYmuXbvCxsYGhw8fxosvvlj5s1WrVqGsrAwff/yxWn2Wl5drtCEHiTNy5Ehs27ZN7hhUje3bt+PMmTNYuHBh5WvFxcUYNGgQzp8/j/j4+Bpv4UxkTFjYJZaamopevXqhadOmOHjwIOzs7AAAubm5aNSoEa+pG4i9e/fCx8dH7hhGLT09HZaWlho9oS03N7fyPVZSUoIhQ4YgMTERsbGx6NKli1RRiQwKb3eTWNu2bREXF4fs7Gz0798f9+7dAwDY2dlpXNQvXLiAvXv3ShGTnoNFXbsEQcBnn32G0tJSjfqpKOqlpaUYOnQoTp06hejoaBZ1Mmks7Frg7OyMuLg4pKenY8CAAZXFXVOtW7dGamoqlEqlJP0RycXMzAy//PILWrZsqXFfFUX92LFjiIqK4sN7yOSxsGtJhw4dcPDgQaSlpaFfv364e/du5c9mzZqFnJwctfu0srLCp59+ylXyRP9TUlICT0/PyqLeq1cvyfoW+z4lkhsLuxa5urri0KFDyMrKQt++fSs/JHx8fLBu3TpJzpGXlydJP1QVd56TVkZGBkaOHPnEbouaKCoqwpAhQ5CQkICYmBj06dNHsr4Bad+nRLrEwq5lLi4uOHz4MO7cuYNu3brh+vXr6Nq1KxISEqBSqTTqu2Lnu4SEBInSUoWVK1fKHcGo2NjYYNGiRZLd4ZGTk4M+ffogKSkJ+/btQ48ePSTp93FSvU+JdI2r4nXkxo0b8PDwQGFhIWJiYnDq1Ck0atQIw4YN06hflUoFlUrFrTLJZDz+XoqOjsabb76ptXOtX79ekvcpkS5xxK4jLVu2xLFjx+Do6IiePXvCwcEBoaGhGvdrbm7Ook56JyUlBZGRkZL3e/bsWXTt2hUAcPz4ca0WdQAYO3asJO9TIl1iYX+GGTNmSN5nkyZNKveT9/HxQXl5OS5duiTpOcLCwjBv3jxJ+yRS19GjR+Hu7i5pn4cPH0bPnj1hb2+PY8eOoVWrVgC0816tYG1tjRYtWkj+PiXSJhb2Z7h//75ax+/YsaNGx9na2iIyMhLDhg1DVFQU/Pz8xMR7pqFDh2LUqFGS9kmkLn9/f402nvm7Xbt2YeDAgejUqRMOHTqEJk2aVP5M3fequvz8/LBq1SqtnoNISizsEvn9999rfKyVlRVCQ0MxY8YM/PHHH/Dz85N0tbCTk5NkfZmqadOmyR3BYKhUKuzdu1fUs9Jr0vc333yD4cOHY9iwYYiMjIStra3k56lO27ZtkZWVheLiYp2el0gsFnaJqLurnLm5OX744QdMnToV69evx4ABA3Dnzh2tZPvkk0/w3//+Vyt9Gys3Nze5IxiMY8eO4fbt25L3W1hYiBEjRuCLL77AV199hdDQUFhZWUl+npoYP348Nm3aJMu5idTFwi6z1atX46233sLFixfh7u6O06dPS36OuXPn8lnUapLi0aGmokePHvDz85P0OQjXrl1Dly5dsH//foSFheGLL76Aubl8H1fe3t6IiIiQ7fxE6mBhl5m5uTnc3Nywc+dONGnSBN26dcNvv/0m6Tns7OzQtm1bSfsk0xUZGYmsrCyt9R8bGwt3d3eUlZUhISEB3t7eWjtXTZmbm6NFixa4du2a3FGInouFXSJiry+qVCpcv34dPXr0wJEjR/Dee+9h7Nix+M9//gOFQiFxykcKCwvh4+Oj1Q9nMk5FRUU4c+YMGjZsKHnfgiBgyZIlGDx4MLp27YqTJ0+iXbt2kp9HjIr36auvvip3FKLnMokboLdv3449e/Y8c6pQEASYmZlhzJgx8PT0rLYvhUKBESNG4OHDh1Xap6Sk4J133qnymoODA9avX19tf2FhYZUjkrp162Ljxo1wc3PDv//9b5w9exZbt25Fo0aNavpHrRFbW1usXr1a8n6NyenTp3md/SlsbGzw2WefSd5vSUkJfH19sWXLFgQGBuLrr7/W+JkIUr7vH3+fEuk9gZ5q4sSJWj2+go+Pj1BUVPTE63FxcYKdnZ3QqlUr4dy5c6L6VsfDhw+F+/fva/08hsLLy0vuCLJTqVTCkiVLhJiYGK2e5+bNm8Ibb7whWFtbC9u3b1e7vdj3njqe9T4l0kecipeIIGIqPjU1FY6OjqhXr94TP+vbty9OnToFW1tbdOrUCUFBQVrdszojIwMjRoxAUVGR1s5hSIKDg+WOIDszMzO8/fbbGDBggFb6FwQBmzdvxptvvomCggKcOHECI0aM0Mq5NFHd+5RIH7GwS0TMiuA1a9YgICDgmT+v2IbW19cX06dPR+/evXH16lVNYj5Tq1atEB0dDRsbG630b2gaN24sdwSdUygUuHfvXpXXevTooZXV6NnZ2fDx8cG4ceMwePBgJCYmwtXVVfLzSOF571MifcPCLhF1R+zFxcVIT09/7mYy9erVQ1BQEA4fPozMzEy4urpqbfT+9y8nZ86cQVBQEMrKyiQ/F+mfKVOmIDExUavnqBilOzs7IyEhAXv27MHmzZv1dr1HTd+nRPqEhV0i6o7YQ0NDMW7cuBof36tXL5w7dw6TJk3S+ui9gouLC5o3b67xIiYyDMHBwfDw8NBa/38fpZ8/fx4+Pj5aO58U1H2fEukDFnaJzJo1S63jw8LCMHToULXa1KtXDytWrNDJ6B0ALCws4OPjU6Ww5+fnIzU1VSvn0ydffvml3BG0at68edi9e7dOzvWsUbqdnZ1Ozq8JMe9TIrmxsD+DulPr6kzVHT16FN26dRN97fLvo/c+ffrobOOMkpISLFu2DAUFBTo5n1yMfae+MWPG4B//+IfWz6OLUbqYhas1oen7lEgu/I19hgYNGmit78jISEyZMkWjPh4fvWdkZMDV1RUrVqzQ6sp5AHj55Zexbt26Kn8/KpXK6Da7+fTTT+WOIIny8nIEBQUhISGhyuuvvfaapFvA/p0uR+naeq9K8T4lkoOZoK2vu6QzxcXFmD17NlauXImePXsiODhYpztk5efnY9q0aZg7dy7at2+vs/PS8wmCgJiYGPTr109nD1DJzs6Gn58fwsPDMWbMGAQFBRnEtDuRseCI3Qg8bfS+ePFilJaW6uT8DRs2xObNm58o6ufOnYNSqdRJBgL++usvfPLJJ8jJyal8zczMDIMHD9ZJUVcoFPjpp58M8lo6kTFhYTciFdfeJ0+ejLlz5+K1117Dzz//rLU9558nOjoa4eHhspxbU2lpaXJHUFudOnXwwQcf4MUXX9TpeQVBwM6dO+Hs7IypU6fC09PTIFa8ExkrTsUbqatXr+Lzzz/H1q1b4eTkhAULFuAf//iHVq+r1sTOnTtha2uLgQMHyprjeby9vfX6S8nOnTsRFRWFkJAQWXPExcVh9uzZSExMxODBg7Fw4UK88cYbsmYiMnUcsRup1q1bY8uWLUhKSsIrr7yCYcOGoXPnzjh06JCsuTp37gxLS8sqrykUCq0v+lPX4sWL5Y5Q6eLFi0hOTq7ymre3t6xFPSkpCR4eHujfvz8sLCxw+PBh/P777yzqRHqAhd3Iubm5ISYmBgcPHgTwaA/6QYMG4b///a8seRwcHNC3b98qr6WmpmLIkCHIy8uTJdPTyLXTmEqleuL2rdjY2Cd2/9PVQri/u3LlCkaOHAl3d3dkZGRgz549OH78OHr16iVLHiJ6Egu7iejTpw/+/PNP7Nq1Czdv3oSbmxtGjx6ts/vfq+Ps7Izo6Gi88MILVV739/dHVFSUTKl07+LFi/Dy8sJff/1V5fXp06ejY8eOMqV6JCsrC35+fmjXrh1OnDiB4OBgnDt3Dj4+PrJf3iGiqniN3QQpFAps3LgR8+bNw19//YUpU6bg888/x0svvSR3tCrKyspQVFRUZR/x2NhYHDhwAIsWLTLogrJw4UKUl5fr/Q53+fn5WLRoEZYvX466deti7ty5CAgIQJ06deSORkTPovMHxZLeKCkpERYvXiy88MILgrW1tTB79mwhPT1d7ljVKi8vF65cufLE66NHjxZ2795d5bX8/HwhOztbUKlUap8nKChI7TbXr18XkpOTq7yWlpYmvPPOO8LFixervC4mky7duXNHWLhwYeXvxty5c4X8/Hy5YxFRDbCwk5CXlyfMmTNHsLGxEWrVqiW8++67woEDB/S++PydUqms8v/Hjh0T/Pz8njjO19dXCA0NrfLa+fPnhS+++EIoLi4WBEEQZs6cKQiCIKxbt07Ytm1blWNTU1MFLy8v4caNG1Ve37Jli7Bz505N/xiyUalUwp9//ilMmDBBqF27tlC7dm3B399fyMrKkjsaEamBU/FU6f79+wgNDcXq1atx/vx5tG3bFv7+/nj//ffRsGFDueNJRhAEqFSqJx5uc+PGDXTo0AEWFhaVr1+7dg116tSBvb29HFF1oqSkBFu2bMHq1atx+vRptGzZEv7+/pg4caJJPpeeyNCxsNMTBEHA0aNHsXr1auzatQuWlpYYO3YsAgIC8Oabb8odjySSmpqKtWvXIiQkBPfv38eQIUMQEBCAgQMH8sEnRAaMhZ2qdfv2bWzYsAHr1q1DRkYGOnfujICAAIwYMYILqAyQQqFAREQEVq9ejQMHDqBx48bw9fXFlClT0LJlS7njEZEEWNipRhQKBSIjI7F69Wrs378fdnZ2mDRpEqZOnYpWrVrJHU9yJSUlRvXo1uzs7MovaJmZmejSpQsCAgIwfPhwfkEjMjIs7KS2y5cvV07hFhQUYMCAAXj33Xfh6elpNNei9X1L2Zq4e/cuoqKisHfvXkRGRsLKygpjx46Fv78/L6kQGTEWdhKtpKQEW7duxaZNmxAfHw+lUgl3d3d4eXnB29sbr7/+usHeax4fH4/u3bvLHUNtqampCA8PR3h4OI4fPw6VSoVOnTph9OjRRrcIkoiejoWdJHHv3r3Kp7lFR0ejsLAQjo6O8Pb2hre3N3r16oXatWvLHdPoKBQKHD9+HOHh4YiIiMDly5dRt25dDBgwAF5eXvD09NS7jYeISLtY2ElyZWVl+OOPPxAREYHw8HDcunULtra2GDRoELy9vTF48GA+o1sDhYWF2LdvH8LDwxEVFYV79+6hadOmlTMl/fr1M6r1AUSkHhZ20ipBEJCcnFw5PXzq1CmYm5uje/fu8Pb2Rs+ePeHq6srRfDXKy8tx4cIFxMfHIyIiAocOHUJZWRk6dOgAb29veHl54a233uItakQEgIWddCw7OxuRkZEIDw/HgQMH8ODBA1haWsLFxQUdO3as/EfuYr9lyxaMHj1a5+etKOJJSUlISkpCYmIizp49i4cPH8LCwgK9e/eGl5cXvLy8eHsaET0VCzvJprS0FOfOnassYklJSUhJSYFSqYSFhQU6dOggW7GfOHGi1p93/ngRT0xMRFJSUmURNzMzg5OTU+Wf3d3dHW+88QZsbGy0momIDB8LO+mV5xV7FxcXuLu7w83NDa+++irs7e3h4OCA+vXr6+0K/KKiImRkZCAzMxM3btzA6dOnWcSJSGtY2EnvVVfsK9SrVw8ODg6Vhf7v/37xxRdha2sLW1vbKnvBi6VUKlFYWIiioiLcvXu3snA/7d/379+vbMciTkTaxsJOBqmsrAxZWVmVxfNpBTUrKwsKheKJtrVr164s8ra2trCxsYGlpSXMzc0r/1GpVJX/KBQKFBUVVRbywsJClJaWPtGvubk5mjVrVu0XDHt7e+70RkRaxcJORkulUiEnJwcZGRnIzc2tUpgf/++ioiKUl5dXKeaPF3kLCwvY2NjAxsamypeBin83atQIDg4OaNq0qSSzAUREmmBhJyIiMiK88ZWIiMiIsLATEREZERZ2IiIiI8LCTiTSrFmzkJOTI3cMIqIqWNiJRPLx8cG6devkjkFEVAULO5FIXbt2RUJCAlQqldxRiIgqsbATaWDo0KHYs2eP3DGIiCqxsBNpYOzYsQgNDZU7BhFRJRZ2ov+ZMWPGU1+Pi4tD7969n/oza2trtGjRApcuXdJiMiKimuP+l0T/8/jDWgBgx44d+P3331FUVIS0tLRntvPz88PKlSuxYsUKbUckInoujtiJnmHEiBEICQmBp6dntce1bdsWWVlZKC4u1lEyIqJnY2EnksD48eOxadMmuWMQEbGwE0nB29sbERERcscgImJhJ5KCubk5WrRogWvXrskdhYhMHAs7kQRUKhWuX7+OV199Ve4oRGTiuCqejNL27duxZ88emJmZPfXngiDAzMwMY8aMee7iuJoICwuDt7e3xv0QEWmKhZ2M0nvvvYf33ntPZ+fbtGkTN6ohIr3AqXgiDaWmpsLR0RH16tWTOwoREQs70fMolcpqH/SyZs0aBAQE6DAREdGzcSqe6BliYmKwYcMGxMfH486dO+jRowecnJywfv36ymOKi4uRnp4OJycnGZMSEf0/FnaiZxg0aBAGDRpU7TGhoaEYN26cjhIRET0fCzuRBsLCwhAZGSl3DCKiSrzGTvQ/giCodfzRo0fRrVs3mJvzbURE+oOfSET/06BBA7WOj4yMxJQpU7SUhohIHDNB3WEKERER6S2O2ImIiIwICzsREZERYWEnIiIyIizsRERERoSFnYiIyIiwsBMRERkRFnYiIiIjwsJORERkRFjYiYiIjAgLOxERkRFhYSciIjIi/weIBoApJP87cAAAAABJRU5ErkJggg==",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000020A4E0B8>)"
      ]
     },
     "execution_count": 48,
     "metadata": {
      "comm_id": "bc91f77b-4978-443c-b138-931df06dc11d",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measurement_plot() # load the interactive plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style=\"color:#00A6D6;\">Global phase is irrelevant</h4>\n",
    "\n",
    "Is there a difference between the qubit $|\\psi\\rangle$ and $|\\phi\\rangle = e^{i\\gamma} |\\psi\\rangle$ for some angle $\\gamma \\in \\mathbb{R}$? It turns out that such a global phase $e^{i\\gamma}$ is irrelevant: there is no measurement that will give us any information on such a global phase - or, in other words - a global phase leads to no observable differences as we explain in detail in the lecture notes.\n",
    "\n",
    "Let's try and convince ourselves below by means of some examples, by measuring a qubit, and the one with the global phase in the standard basis. Of course, you may wish to measure in other bases as well!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Complex{Float64},1}:\n",
       " 0.703574+0.0705929im\n",
       " 0.703574+0.0705929im"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Basis to measure in - default is the standard basis\n",
    "b0 = [1; 0];\n",
    "b1 = [0; 1];\n",
    "\n",
    "# State to be measured - default is the plus state\n",
    "psi = [1; 1]/sqrt(2);\n",
    "\n",
    "# Set the global phase\n",
    "gamma = 0.1;\n",
    "phi = e^(im * gamma) * psi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Float64,1}:\n",
       " 0.707107"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the outcome probabilities\n",
    "\n",
    "val = b0'*psi;         # note, we compute the inner product by multiplying\n",
    "                       # a row vector - here b0' (note the accent: b0' is the hermitian transposes of b0)\n",
    "                       # and a column vector - here psi.\n",
    "                       # This returns a 1-element array - here val. \n",
    "                       # val[1] returns the first and only entry of this array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Without phase: p0 = 0.5\n",
      "\n",
      "With phase: p0 = 0.5\n",
      "\n"
     ]
    }
   ],
   "source": [
    "p0 = abs(val[1])^2;    \n",
    "\n",
    "val = b0'*phi;\n",
    "p0Phase = abs(val[1])^2;\n",
    "\n",
    "# Round and print\n",
    "digits = 3;\n",
    "p0 = round(p0,digits);\n",
    "p0Phase = round(p0Phase,digits);\n",
    "\n",
    "println(\"Without phase: p0 = \", p0, \"\\n\")\n",
    "println(\"With phase: p0Phase = \", p0Phase, \"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\"> edX Exercise 4 </h3>\n",
    "\n",
    "Consider the measurement basis \n",
    "\n",
    "$$ \\{ \\left| b_0 \\right\\rangle , \\left| b_1 \\right\\rangle \\} $$\n",
    "\n",
    "with\n",
    "\n",
    "$$ \\left| b_0 \\right\\rangle = \\sqrt{\\frac{1}{3}} \\left| 0 \\right\\rangle + \\sqrt{\\frac{2}{3}} \\left| 1 \\right\\rangle$$\n",
    "\n",
    "and \n",
    "\n",
    "$$\\left| b_1 \\right\\rangle = \\sqrt{\\frac{2}{3}} \\left| 0 \\right\\rangle - \\sqrt{\\frac{1}{3}} \\left| 1 \\right\\rangle$$\n",
    "\n",
    "For different states $ | \\psi \\rangle$ calculate probabilities of obtaining measurement outcomes 0 and 1. That is, compute the exact probabilities\n",
    "\n",
    "$$ P(B=0) = p_0 = |\\langle b_0 | \\psi \\rangle|^2 $$\n",
    "\n",
    "and \n",
    "\n",
    "$$ P(B=1) =  p_1 = |\\langle b_1 | \\psi \\rangle|^2 \\:.$$\n",
    "\n",
    "for each of the following states\n",
    "\n",
    "$$ |\\psi_1 \\rangle = |0\\rangle$$\n",
    "\n",
    "$$ |\\psi_2 \\rangle = |+\\rangle$$\n",
    "\n",
    "$$ |\\psi_3 \\rangle = |-\\rangle$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Feel free to use some code to check yourself"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style=\"color:#00A6D6;\"> Supplement no. 1 to Exercise 4 </h4>\n",
    "\n",
    "The code below can be completed to calculate the answers to exercise 4 numerically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: UndefVarError: .. not defined\nwhile loading In[53], in expression starting on line 7",
     "output_type": "error",
     "traceback": [
      "LoadError: UndefVarError: .. not defined\nwhile loading In[53], in expression starting on line 7",
      ""
     ]
    }
   ],
   "source": [
    "# This is the basis we will measure in\n",
    "b0 = [1/sqrt(3); sqrt(2/3)];\n",
    "b1 = [sqrt(2/3); -1/sqrt(3)];\n",
    "\n",
    "# Define the states\n",
    "psi1 = [1; 0]; # write down the state vector for |0>\n",
    "psi2 = [..; ..]; # write down the state vector for |+>\n",
    "psi3 = [..; ..]; # write down the state vector for |->\n",
    "\n",
    "# Write code to compute the probabilities - we'll do it for just one of the cases here.\n",
    "val = b0'*psi1;\n",
    "p0GivenPsi1 = abs(val[1])^2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style=\"color:#00A6D6;\"> Supplement no. 2 to Exercise 4 </h4>\n",
    "\n",
    "It is helpful to visualize the measurement. Run the code below by clicking inside the block of code and pressing shift+enter.\n",
    "\n",
    "You will see a 2D plot of $\\left| b_0 \\right\\rangle$ and $\\left| b_1 \\right\\rangle$ appear. \n",
    "\n",
    "Furthermore a slider labeled $\\theta$ will appear which allows you to select $|\\psi \\rangle = |0\\rangle$, $|\\psi \\rangle = |+\\rangle$ or $|\\psi \\rangle = |-\\rangle$.\n",
    "\n",
    "Accordingly $|\\psi \\rangle$ is plot together with a numerical approximation of \n",
    "\n",
    "$$ p_0 = |\\langle b_0 | \\psi \\rangle|^2$$\n",
    "\n",
    "and \n",
    "\n",
    "$$ p_1 = |\\langle b_1 | \\psi \\rangle|^2 \\:.$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000026169E80>)"
      ]
     },
     "execution_count": 54,
     "metadata": {
      "comm_id": "216b2318-8876-47b3-8fde-c5a45def40b3",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "projective_measurement_plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\"> Measuring two qubits</h3>\n",
    "\n",
    "Let's now imagine we have two qubits A and B. We will imagine that Alice holds qubit A and Bob holds qubit B. Evidently we might imagine that Alice measures her qubit in a basis... and also Bob could measure his qubit in a basis. What can we say about the overall measurement? \n",
    "\n",
    "Let's consider the example where Alice measures in the in the standard basis\n",
    "\n",
    "$$ |0\\rangle_A = |0\\rangle \\\\ |1\\rangle_A = |1\\rangle$$\n",
    "\n",
    "and Bob measures in in a \"$\\pi/8$ rotated\" basis:\n",
    "\n",
    "$$ |0_L\\rangle_B = cos \\frac{\\pi}{8} |0\\rangle + sin\\frac{\\pi}{8} |1\\rangle \\\\ |1_L\\rangle_B = -sin\\frac{\\pi}{8} |0\\rangle + cos \\frac{\\pi}{8} |1\\rangle$$\n",
    "\n",
    "To see how this is a \"$\\pi/8$ rotated\" basis consider the following picture, where we will actually plot the basis of Alice and Bob into the same plot even though they are of course on two different qubits.\n",
    "\n",
    "<b> In case you see no image, click in the code block below and press shift+enter, it might take a moment before the resulting image is loaded</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000002091C2B0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x00000000260C50F0>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi8_rotated_basis_plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\">edX Exercise 5 </h3>\n",
    "\n",
    "How can we describe the overall measurement if Alice measures in the basis $\\{|0\\rangle_A, |1\\rangle_A\\}$ and Bob - as defined just above - measures in the basis $\\{|0_L\\rangle_B,|1_L\\rangle_B\\}$  ?\n",
    "\n",
    "Clearly we expect the overall measurement to have 4 outcomes, 0 or 1 for Alice, as well as 0 and 1 for Bob. This is indeed the case, and we can compute the outcome probabilities by taking the basis for Alice and the one for Bob, and constructing the basis for both qubits together.\n",
    "\n",
    "This can be done using the tensor product. Find the <b> measurement basis for A and B combined_L</b>:\n",
    "\n",
    "1. $|0\\rangle_A \\otimes |0_L\\rangle_B$\n",
    "2. $|0\\rangle_A \\otimes |1_L\\rangle_B$\n",
    "3. $|1\\rangle_A \\otimes |0_L\\rangle_B$\n",
    "4. $|1\\rangle_A \\otimes |1_L\\rangle_B$\n",
    "\n",
    "For clarity we have filled in the first coefficient for the first listed tensor product:\n",
    "\n",
    "1. $|0\\rangle_A \\otimes |0_L\\rangle_B = \\begin{pmatrix} cos(\\frac{\\pi}{8}) \\\\ ? \\\\ ? \\\\ ? \\end{pmatrix}$\n",
    "\n",
    "Find such exact vector representations for the tensor products (1.), (2.), (3.) and (4.)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To check your answer, use the Julia snippet below!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[56], in expression starting on line 11",
     "output_type": "error",
     "traceback": [
      "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[56], in expression starting on line 11",
      ""
     ]
    }
   ],
   "source": [
    "# Let's first define Alice's basis. She measures in the standard basis\n",
    "alice0 = [1 ; 0];\n",
    "alice1 = [0 ; 1];\n",
    "\n",
    "# Let's now define Bob's basis.\n",
    "bob0 = [cos(pi/8); sin(pi/8)];\n",
    "bob1 = [- sin(pi/8); cos(pi/8)];\n",
    "\n",
    "# Compute the combined basis - your code goes here!\n",
    "cb_1 = kron(alice0,bob0)\n",
    "cb_2 = ...\n",
    "cb_3 = ...\n",
    "cb_4 = ...\n",
    "\n",
    "# To print, let's round \n",
    "digits = 3;\n",
    "cb_1r = round(cb_1,digits);\n",
    "cb_2r = round(cb_2,digits);\n",
    "cb_3r = round(cb_3,digits);\n",
    "cb_4r = round(cb_4,digits);\n",
    "\n",
    "println(\"combined basis (1.): $cb_1r^T \\n\")\n",
    "println(\"combined basis (2.): $cb_2r^T \\n\")\n",
    "println(\"combined basis (3.): $cb_3r^T \\n\")\n",
    "println(\"combined basis (4.): $cb_4r^T \\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\"> edX Exercise 6 </h3>\n",
    "\n",
    "Suppose now that Alice and Bob measure in the basis we constructed above. And let's suppose they measure the EPR pair \n",
    "\n",
    "$$ | \\Phi \\rangle = \\frac{ |0\\rangle \\otimes |0\\rangle + |1\\rangle \\otimes |1\\rangle}{\\sqrt{2}} = \\frac{1}{\\sqrt{2}}\\begin{pmatrix} 1 \\\\ 0 \\\\ 0 \\\\ 1\\end{pmatrix}\\:.$$\n",
    "\n",
    "What are the probabilities \n",
    "\n",
    "$$ p_{xy} = \\Big|\\big( \\langle x \\rvert_A \\otimes \\langle y_L \\rvert_B \\big) \\cdot | \\Phi \\rangle \\Big|^2$$\n",
    "\n",
    "of Alice getting outcome $x \\in \\{0,1\\}$ and Bob outcome $y \\in \\{0,1\\}$ rounded to 3 digits ?\n",
    "\n",
    "In other words, what are \n",
    "\n",
    "1. $ p_{00} = \\Big|\\big( \\langle 0\\rvert_A \\otimes \\langle 0_L \\rvert_B \\big) \\cdot | \\Phi \\rangle \\Big|^2$\n",
    "2. $ p_{01} = \\Big|\\big( \\langle 0\\rvert_A \\otimes \\langle 1_L \\rvert_B \\big) \\cdot | \\Phi \\rangle \\Big|^2$\n",
    "3. $ p_{10} = \\Big|\\big( \\langle 1\\rvert_A \\otimes \\langle 0_L \\rvert_B \\big) \\cdot | \\Phi \\rangle \\Big|^2$\n",
    "4. $ p_{11} = \\Big|\\big( \\langle 1\\rvert_A \\otimes \\langle 1_L \\rvert_B \\big) \\cdot | \\Phi \\rangle \\Big|^2$\n",
    "\n",
    "rounded to 3 digits? \n",
    "\n",
    "Help yourself by making use of some code, we have made a draft below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[57], in expression starting on line 11",
     "output_type": "error",
     "traceback": [
      "LoadError: syntax: invalid identifier name \"...\"\nwhile loading In[57], in expression starting on line 11",
      ""
     ]
    }
   ],
   "source": [
    "## in case you have succesfully ran the previous code block\n",
    "## the combined basis cb_1 till cb_4 should be defined.\n",
    "\n",
    "## Then let us define the state to be measured\n",
    "\n",
    "Phi = [1;0;0;1]/sqrt(2);\n",
    "\n",
    "# The probabilities follow from the squared inner product\n",
    "# betweeh Phi and the measurement basis \n",
    "p_00 = abs(Phi'*cb_1).^2\n",
    "p_01 = ...\n",
    "p_10 = ...\n",
    "p_11 = ...\n",
    "\n",
    "# We will round the probabilities to 3 digits\n",
    "digits = 3;\n",
    "\n",
    "p_00 = round(p_00,digits)\n",
    "p_01 = ...\n",
    "p_10 = ...\n",
    "p_11 = ...\n",
    "\n",
    "println(\"p_00: $p_00 \\n\")\n",
    "println(\"p_01: $p_01 \\n\")\n",
    "println(\"p_10: $p_10 \\n\")\n",
    "println(\"p_11: $p_11 \\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----\n",
    "<a id=\"transformations\"></a>\n",
    "<h2 style=\"color:#00A6D6;\">Unitary Transformations</h2>\n",
    "\n",
    "You have learned in class that transformations on qubits, are given by unitary transformations. Let's investigate such transformations in detail. \n",
    "\n",
    "As a warmup let's just define a matrix - the Hadamard transform, and verify that its indeed a unitary\n",
    "\n",
    "$$H = \\frac{1}{\\sqrt{2}}\\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2x2 Array{Float64,2}:\n",
       " 0.707107   0.707107\n",
       " 0.707107  -0.707107"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define the Hadamard transform as a matrix in Julia\n",
    "tH = [1 1;1 -1]/sqrt(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2x2 Array{Float64,2}:\n",
       " 1.0  0.0\n",
       " 0.0  1.0"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's now check whether the transformation is unitary by computing U' * U\n",
    "U = tH;\n",
    "U' * U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2x2 Array{Float64,2}:\n",
       " 1.0  0.0\n",
       " 0.0  1.0"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# And also U * U'\n",
    "U * U'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an exercise, you may wish to convince yourself that the Pauli matrices: X, Z and Y - as defined below in the Julia code - are also unitary!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Pauli X\n",
    "pX = [0 1;1 0];\n",
    "\n",
    "# Pauli Z\n",
    "pZ = [1 0;0 -1];\n",
    "\n",
    "# Pauli Y\n",
    "pY = im * pX * pZ;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us vizualize the effect of a unitary transformation $U$ on $\\lvert \\psi \\rangle$. What does $U|\\psi\\rangle$ look like?\n",
    "\n",
    "$$\\lvert \\psi(\\theta) \\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\end{pmatrix} = \\begin{pmatrix} \\cos\\theta \\\\ \\sin{\\theta} \\end{pmatrix} $$\n",
    "\n",
    "\n",
    "<b> Click in the code block below and press shift+enter.</b>\n",
    "\n",
    "You will see a slider appear which lets you pick $\\theta$.\n",
    "\n",
    "The state vector $\\lvert \\psi(\\theta) \\rangle$ is plotted accordingly.\n",
    "\n",
    "Click the check-box to apply the unitary transformation (by default the Hadmard transformation) to $\\lvert \\psi(\\theta) \\rangle$ and you will see the resulting state vector $U \\lvert \\psi(\\theta) \\rangle$ plotted as well.\n",
    "\n",
    "Vary $\\theta$ to see how $U \\lvert \\psi(\\theta) \\rangle$ and $\\lvert \\psi(\\theta) \\rangle$ change accordingly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Slider{Int64}(Signal{Int64}(0, nactions=0),\"θ\",0,-180:15:180,true)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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rf46Ojsa0adNKrfPUqVMwMzPDvHnzwDAMRCIRCgoKEB0djY4dO5a43sXFpdypklZWVmjTpg2CgoLQs2dPTV6q1lGiYEACAgIwbdo05OXlYfv27Zg8eTKMjXX3T/zu3TuVb71t2rTB2bNneUlSKksoi6F8+O8bGBiI5ORkLFu2TGcxiEQieHh4oGfPnvDz88M333wDFxcXbNq0CePGjRPkv78hk2c8Qfah3jq/r8XoCzC2aaWTe926dQvu7u4wMTFBUFCQSldrVFQUJkyYAOB9C+emTZtw7Ngx5fnExMRSux0YhsHVq1cxZMgQHDhwQHk8MDAQwcHB6N69e4kyVlZWKkmIOgzDlFgATp9QosCDhQsXYv78+ahXrx4n9b158wZz5szBgQMH0L9/f/z+++86/za3c+dOxMfHY926dcpjukxSuObg4MB3CBrx9vYucezFixewsLBAjRo1tHpvsViMUaNGwcPDA3PnzsWECRNw9OhRXt6PXOD6c6ovjKydYDH6Ai/31RVHR0e0bt0aL1++RGBgII4fP648J5fLVZJXOzs7tG3bVvnz27dvS00UUlJSkJmZiQ4dOqgcP3fuHEQiEYYOHVqijLW1dYnF2j6UkZGBiIgIbN++vcKvT9eE+yQXsEGDBuH333/Hd999V+m6irci7N27V2ff4ORyucpgnqlTp2r9nkQzT548wb59+3TWD2ptbY39+/dj+PDhmDp1qmBbF7j8nOoTkYm5zr7Z86Vos7pjx46hevXq6NOnD4D3Y4+cnZ1Vro2IiMDgwYOVP4tEIpVBiUVevnwJAGjRooXymFwux9GjR9G5c2d88sknJcqIxeJyWwp+//13TJkypYKvjB80mJEH7u7uuHXrVqlvxop68+YNxo0bBy8vL7i6uuL+/fsYP368Th7E33//PTZu3Kj1+xBudOrUqUSSIJVKK/X+qwhPT0/cv38fXl5emDBhAjw9PSGRSLR6Ty5x8Tkl/AoLC0O7du2Ugww/7CKQSqVITk5W2QW3du3ayMjIKFGXsbExRCIR6tevrzx27tw5vHr1Cj/++GOp93/9+jUsLS3VxieTyeDr64vx48ezfm26RIkCTwYOHIiTJ09qVDYgIAAuLi7w9/fH3r17ERAQoNOm3aVLl2L+/Pk6ux8finehGKK7d+/C09OzxGBIrhW1Lvj7+yMqKgouLi7Yt2+fYKZSVuZzSviXk5MDKysr5c/37t1Dy5YtAbwfF7Bq1Sp8/fXXKmU+/vjjUhOFou7I4l2qv/zyC6ZOnYpOnTqVev+MjAw4Ojqqjc/Pzw8DBgyAmZlZhV8THyhR4Mno0aNx8OBBVmWKtyJ89tlnOmlFOHjwYIlvo0Iee1BReXl5fIegVe3atUNAQIDO/i2F2rqgyeeU6I+RI0ciNDQUL168UDmelpaGhQsXYty4cSW+8Xfq1KnUtQ+sra3RoUMH5dTp3bt3o6CgAJs2bVJ7/7i4uBKrrxa3detWzJo1i81L4gUlCmpoe/Efc3NzODo6Vni+/oetCGfOnNFJK0Lz5s31vllMG1auXMl3CFr34RTKW7duYc2aNVprZdBW64I2P6tsP6dEv4wePRo///wzRo8ejbFjx+LZs2dYvXo1Dh06hBUrVsDJqeQAyz59+iA0NLTU+nbu3ImdO3fCx8cH//zzD0JCQpRTvz/EMAyuX79e6mwI4H23SKNGjWBra6v5C9QVbS0PKXTe3t5av0dsbCwza9asMq958+YNM3bsWAYA069fPyYlJUVr8RQUFJS74xkxXAqFggkKCip3IxsuvH79WuV9/fz5c43rYvNZ9fPzY11/RT6nfKAlnFWVt4Tzli1bmPv375dbj1QqZerUqVPpzZoiIyMZJycnteeHDRvGREREVOoelUFLOAtEs2bN8Pz58xKbIRV5+PAh2rVrp7NWhO+//x53797VWv1Ev4lEIvTo0UOlKysnJ0crLQzFWxeio6Ph6uqKGzducH6fD2mykmV5n1MiDDExMSozFtQxNTXFzJkzy+xSqIht27apbe1KTEzEq1ev0KZNm0rdQ1coUeDZ2LFjS13n+/Tp02jfvj1MTU0RGRmpkxkNP/zwAwYNGqTVewhFeno63yHohbt372LkyJFaG3zo6emJv//+G40bN0bXrl3x559/auU+RTT9DKn7nBLhYPNvv2DBApw7d67cNRDUSUpKKnOFx82bN3O+Q602UaLAMy8vLwQEBCh/VigUWLlyJQYNGoSePXvixo0bpfajVVZ8fDx+//13zus1FBMnTuQ7BL3QsWNHHD16VKtJav369REcHIyJEydiypQpmDlzZomtxfn24eeUCMv9+/dZ7S9To0YN7Ny5U6P1DeRyOWbOnIl9+/aVOlg4JycHly9fxpAhQ1jXzRdKFHgmFovh6OiI+Ph4ZGVlYciQIVixYgV++OEHHDt2DBYWFlq576NHj9QOsiHAihUr+A5Bb3w46DE6OhqZmZmc3sPU1BQ7duzAjh078Mcff6Bnz55IS0vj9B6VUfxzSvSTpaWl2mmGLi4umD59Oqv62rdvj0mTJrFezn316tWYO3eu2sTk/PnzmDRpkqAWHzP8eW56TqFQICEhAQqFAh06dEBKSgr8/f3h6emp1fv269dPq/ULXVlTmqq6/Px8bNmyRSsrFk6bNg2ffPIJhg4dCjc3N5w6dYrTHU817UIp+pw2btyYs1gIt3799VfO6+zduzd692a3L8aSJUvKnHY8bNiwyoalc1UiUfDz88PJkyfVZnDM/3YB+/LLLzFgwACd1nf69Gk0btwYbdu2hY2NDW7fvl1iidHKSk1NxapVq7Bp0yaVZZcJ0YS7u7vabXi50LFjR0RGRmLIkCHKVSXHjBnDqg6ZTIbhw4dDKpUqjzEMg5iYGJUkmWEY2Nvbl7u89enTp+Hl5cXuhZAqySDXmdHq/AsB08X0SIVCwbRo0YIBwPTv35/JzMzUyn2ePXvGxMTEaKVuQhiGYfz9/ZnCwkJO63z37h0zfvx4BgDz9ddfq62fzWdV08/1oEGDmJycHI3KagtNjySVQdMjBUAmk2HYsGF48OAB/u///g+nT58uc03wyvjPf/4DFxcXrdRtqHbt2sV3CIKSmZmJCxe43ZHQzMwMe/bswaZNm7B582YMHjy40itmMhp0PTx69AgNGzbU+u6bhOgrShR4kJeXh8GDB+PkyZNYu3YtfvzxR866BBiGwZ9//onbt29zUl9VFR0dzXcIgjJ27Fj079+f83pFIhFmz56Ns2fPIiQkBD179ix1HX429bG1fft2+Pj4aHxPQoSOEgUdy8jIQM+ePXH58mW4u7tj0aJFnNbPMAzMzc05HQBWFW3bto3vEAQtMzMTz54946y+3r17Izg4GI8fP0anTp2QnJysUT1sWxRyc3ORnJzM+bghQoSEEgUdSk5ORqdOnRAXF4fZs2dj3rx5nN9DLBbjyy+/pEGLhFc5OTlYsmQJp+shtGvXDmFhYcjLy4O7uzvu37/Pug62LQoHDx5kPZCSEENDiYKOPHjwAO7u7sjLy0NYWBj++ecfDBw4sNL1FhYW0kIwRO/Y29vD19dX7YY5mmratCnCw8NhbW2Nzp07Izw8nFX5hQsXsrr+9OnTnHxOCREyShTU0GTQkzrR0dHo3LkzrKysEB4ejrS0NHTs2LHEQjaaOHv2rMFviUwMA1d7Rtja2iI0NBQtW7ZEjx49kJKSUuGybLoQrl27xtnnlBAho0+AGlzNQIiIiECPHj3g5OSE0NBQ2Nra4syZM5g6dSon9Q8aNAgjR47kpC7yL5ozzz0fHx/OZkbUrl0bFy5cQPfu3REcHIzz589zUm9xXH5OCREyEcPlV2ei4tatW/Dw8ICLiwsCAwM5ST4YhkFhYSHnTbpE1cWLF+Hh4cF3GAZFJpMhOzsbVlZWnNUplUoxfPhwXLhwAcePH6/QgmmGIjo6Gm5uboiKiqKVRAlrbN4/1KKgJbdv34aHhwdatmyJCxcucNZCMWPGDAQHB3NSF1GPkgTuGRsbc5okAEC1atVw7Ngx9OvXD0OHDtVoG2lCSNkoUdCCqKgoeHh44JNPPkFgYCCnGzutWrUKffr04aw+QvgSEhKi0cyFD5mamuKvv/5C3759MWTIEFy8eJGD6AghRShR4Njdu3fRq1cvODs7qyQJz58/52SA5EcffVTpOgjRBy1atMCZM2cqVYdEIgHwb7LQs2dPDBw4kFrdCOEQJQocSkhIQJ8+ffDxxx/j/PnzqFWrlvLc+fPnsWHDBtZ1BgUFVWolOqKZU6dO8R2CwbOxsanUgmOHDx9WWWq7qBuiS5cuGDhwIK2uSQzeiRMnsHnzZq3fhxIFjqSlpaF3796oWbMmAgMDUbt2bZXzEydOxJw5c1jVmZubi4CAAFpjnge+vr58h1AlfdjqVlhYiJycHBQWFpa4dtiwYSW2ujYzM8Px48fRokUL9O3bF/Hx8VqNlxA+9e7dG3v27OF0On9pDHA/TN3Lzs5G//79kZOTg/DwcNSrV6/U69jOVKhRowY2bdrERYiEpb/++ovvEKqc+/fvY8uWLfjtt9+QkpKC8PCbCA+PRX6+AmZmYri7O8PdvQMcHBwAqP881axZE2fPnkWnTp3g4eGB8PBw2NjY6PKlEKITNWrUgIeHB06cOIGhQ4dq7T7UolBJBQUFGDp0KOLi4hAYGIiPP/64QuViY2O1ngUSIiQuLi6YPHkyIiMjsWbNHvj5vUJengdMTb9AXp4H/PxeYeHC9YiMjCy3rjp16uDChQvIz89H3759kZWVpYNXQEjZSmsZq6xZs2Zh69atnNdbHCUKlaBQKDBhwgSEhobi9OnTaN26dYXLhoaGYufOnSrHCgsLMX/+fFppkVRZ9erVw549gcjKaoeWLX1gb98Bdeo0g719B1Sr5oCYmNfYtesskpKSyq3rP//5D86fP4+EhAQMHjwYUqlUB6+AGII5c+YgLS2N0zqPHDmCw4cPsy63fPly3LlzR+35hg0bwsbGBlFRUZUJr0yUKFTC4sWLlf/43bp1Y1V22rRpmDJlisqxrKwsdOvWDebm5hxGSYhwhIffxMuXdeDk9H4KcGHhv0lz06b9MWTIIbx8WQfh4TcrVF/Lli0REBCAsLAweHt7Uyuegbp16xZ69uyJevXqQSwWo379+ujRoweOHz+uvGbXrl1o0qQJxGIxzM3N0aVLF7U7nGZlZSE/P7/C9587d26Z5y9fvozbt29j/PjxpZ5PTEzE9OnTsXjxYowYMQK5ubnKc0uXLsXChQvx9OlTtfXPmTMHGzdurHC8bFGioKHDhw/jp59+wi+//KJx39CHa8h/9NFHVWplOX3m7e3NdwhVTmFhIcLDY2Ft7QaRSITMzKfw9R2O+/ff7xEhEokhFothbe2G8PDYCjfjdu7cGQcOHICvr69GM4+I/mvfvj2CgoIwZMgQiEQiBAcH4/LlyyrP5kmTJuHRo0do1KgRHj9+jKtXr8LR0bHS93758mWZC4m9ffsWS5YswZo1a0o9/+zZMwwdOhQ//PAD1q5diw4dOmDp0qXK89WqVcNvv/2GsWPHqk10P//8cyQlJeHFixeVezFqUKKggejoaEyaNAnjx49nPZNBnVu3btG3HT1CKzPqnlQq/d/AxfcPXSOjRnj16isEBRmj+H5SZmZWkEoVrLoShg8fjqVLl2Lx4sWc7TdB9M+VK1dgY2ODFi1alHo+MzMT7u7usLOz4+yewcHB+O9//6v2/KpVqzBu3DhUq1atxLnCwkIMGzYMc+bMQd26dQEADg4OOH36tMp1Tk5OcHBwKHM2lo+PD7Zs2aLhqygbJQospaWlYdCgQWjZsiV27NjBen/74goKCjBx4kRkZWUhOjoafn5+HEZKKuOLL77gO4Qqp1q1ajAzEyM//w2ysoA//7yOwsJrGDcOMC42Pys//w2qVROX+uAty/fff4++ffti1KhRePLkCcfRE769ePECcXFxZXYDh4aGomvXrpze9+bNm/j8889LPZeXl4c///wTY8aMKfX8r7/+ipcvX+IwYbiaAAAgAElEQVTLL79UHnv79i2Sk5Mhl8tVrp09ezZWr16tNo5hw4bh3LlzWhmLQ4kCC4WFhRgxYgSkUilOnDgBMzOzStUnk8ng7e2NWrVqYcaMGRgxYgRHkRIiPCYmJnB3d4ZEEot9+xiIxZ0wdeqPKGrVlcsLUFj4DhkZUXB3d4aJiQmr+o2MjHDw4EHUq1cPgwYNQnZ2thZeBeFLSEgIAJSZCISEhJT57V8TBQUFat+LAQEBaNy4cYl1dYD3LWjr16/H5MmTYWRkpDweExMD4P1g+eLatWuHlJQUPHjwoNR7GRsbY9SoUdi/f7+mL0UtShRYmDdvHsLCwnD8+HHY29tXuj5zc3N07txZ+XNlWicIMQSNGnXEjRueyM/Px7hxDKyt//1MpKbeweHD/WFjkw539w4a1V+7dm2cOnUKSUlJGD9+fImHMRGukJAQiESiMhOBJ0+eoFGjRqzrTkpKwuzZs+Hp6anS/J+UlKScEl9QUICWLVuqfOu/fPky3N3dS63T19cXGRkZJb4ghoWFwcLCokTyIRaL8fnnn5e5pfrUqVPxxx9/sH595aEFlypoz5492LJlC7Zv345OnTpp/X6BgYHo06cPJQ88uX79uk7+ncm/JBJg8OB7MDPriv79dyIlxRh5eW4wM7NCfv4bZGREoVu3tpg0qb9y0SVNNG/eHAcPHsTAgQOxatWqEqs7Grq8PCA2Vvf3dXYGtDmh68qVK6hfvz6aNm1a6vn09HS1i+GVZ+3atdi0aRN27NiBdevWKbsmL1++rJKYSKVShIeHK3+Ojo7GtGnTSq3z1KlTMDMzw7x588AwDEQiEQoKChAdHY2OHTuWWsbFxaXMqZJWVlZo06YNgoKC0LNnT01eaqkoUaiAW7duYfr06ZgyZYraf/SK+uWXX9CzZ0+0atWqzOuePn2KoKAg9OrVq1L3I5pZv349JQo6JJEA7u73kZNzHdHRvWFiMvh/KzNehFSqgLm5GD17OsPd3bNSSUIRLy8vrFy5EsuWLcOnn34KLy8vDl6FMMTGAm5uur9vVBTg6qqdup8/f44nT56UObYoNDS0xPiF2NhY1K1bt8zN9m7dugV3d3eYmJggKCgITZo0UZ6LiorChAkTALxfKXTTpk04duyY8nxiYmKp3Q4Mw+Dq1asYMmQIDhw4oDweGBiI4OBgdO/evdRYrKysVBKR0jAMU2J8Q2VRolCO1NRUDBkyBG3atMGWLVsq9Q2fYRjY2dmhZcuW5V7r4+Oj8X1I5R05coTvEKoMiQR4/6XMBX///SPetww7wMHBAUOHFkIqlaJatWolmmJlMhmMjTV/hH377be4c+cOxowZg9u3b8PZ2bkyL0MwnJ3f/9Lm477aUtHxCQsWLFD+fPPmTbi7u8PR0REJCQlqyzk6OqJ169Z4+fIlAgMDVdZmkMvlKr8T7Ozs0LZtW+XPb9++LTVRSElJQWZmJjp0UO1CO3fuHEQikdop99bW1nj79q3aWDMyMhAREYHt27ervUYTlCiUQaFQYNSoUQCAY8eOsR5l/SGRSISRI0dyERrRMlr0SjeKkgSpFAgJAT7sPjYxMVE7UGzt2rVwcXHB4MGDNbq3WCzGvn370KFDBwwePBjR0dGoXr26RnUJibm59r7Z8+Xu3bsQiURqWwEZhkF8fDz+85//KI+Zm5ujevXqsLa2LrPuon1Cjh07hurVq6NPn/eLgcXGxpZILiMiIlTejyKRqNRxMC9fvgQAlWmccrkcR48eRefOnfHJJ5+UGotYLC6zteD3338vsZAfF2gwYxk2b96Mq1ev4vDhw2jQoAFvcTAMg0OHDtE6C8SgSCRAmzZ/IT+/sNQkoTyLFi2qUOtcWSwsLHDs2DE8ffq0yo1VMCRFy94X7xYo7uDBgyUWs2vVqhVSU1Nx82bFVvkMCwtDu3btlInrh10EUqkUycnJKhuQ1a5dGxkZGSXqMjY2hkgkQv369ZXHzp07h1evXuHHH39UG8Pr169haWlZ6jmZTAZfX1+1qz9WBiUKajx+/BhLly7FV199Val5t2/evKn0dBWRSKRca4EQQyCRAJ06JePdu1iEhBizThKA960NTk5OlY6lefPm+OGHH/DLL7+U2/9L9JPb/wZdpKenlzj34MEDHD58GDNmzChxrlatWhXuvsrJyVFZgfHevXvKRJVhGKxatQpff/21SpmPP/641EShaJxN8Xv/8ssvmDp1apljozIyMtSuJunn54cBAwZUetp+aShRKIVCocDEiRNha2urdtnNirp06ZLaVcLYmDFjhvLDQLSveF8m4VZRd4NC0RDR0cvRuDH/M3u++eYbtGvXDt7e3nj37h3f4RCWvvjiC7Rq1Qpff/21SstrQEAAvvvuO/j6+pZYMp+tkSNHIjQ0tMQyyWlpaVi4cCHGjRtX4tt+p06dSl33wNraGh06dEDs/6af7N69GwUFBdi0aVOZMcTFxcFVTb/R1q1bMWvWLDYvqcJojEIpNm/ejOvXryM0NBQ1atSoVF20iJIwcTGynpRU3pgETb179w4rVqzA2rVrNRpwbGRkhL1796J169b47rvvaE8IgTEzM8OVK1fw7bffolOnTqhduzbEYjE8PDzg5+ensqCRpkaPHg2GYTB69GjY2toiPT0dq1evRvXq1bFixYpSf1f06dNH7YZRO3fuxOLFixEYGAhTU1OEhITA1NRU7f0ZhsH169dL7SILCwtDo0aNYGtrq/kLLAtDVMTFxTHVq1dnvvrqK75DUUsmkzFbt25lFAoF36EQUmEpKQxTr96fjL19NhMfz339vr6+TGZmZqXqWL9+PSMSiZiwsDCOotKeqKgoBgATFRXFdygGZ8KECUxiYqLa81u2bGHu379fbj1SqZSpU6cOk5qaWumYIiMjGScnp1LPDRs2jImIiGBVH5v3D3U9FCOXy+Ht7V3pLofk5GQUFBRwGJkqIyMjmJiYID4+Xmv3IIRLEgnQpctrSKWvcOVKDc5aEoobNWqU2oFeFUVdEKQiYmJiKtSlbGpqipkzZ5bbpVAR27ZtK7V1IjExEa9evUKbNm0qfQ91KFEoZsuWLQgLC8Pu3bs17nJQKBSYOnUqMjMzOY5O1dSpUzkZyEWIthV1N8hkHyE6erFejElQp6gLIjExkWZBELXYdG8tWLAA586dK3P9g/IkJSWpXeVx8+bN+OqrrzSuuyIoUfif4rMcunTponE9YrEYJ0+e1HipUKIfYvlY49YAaWtMQnkiIiI0Xp3O2dmZZkEQte7fv49PP/20wtfXqFEDO3fu1Hh9A7lcjpkzZ2Lfvn0lZmjk5OTg8uXLGDJkiEZ1VxQlCuCuy6GINqanlCU/Px9r166ldRY4tHDhQr5DEDyJBPjss23Iy3ul0yQBeD8lrjLTkqkLomqztLRU+xx3cXHB9OnTWdXXvn17TJo0CVu3bmUdy+rVqzF37txSk5Pz589j0qRJ2t8TiNXoBwO1ceNGBgATGhrKdyga2717NycDZsh7ZQ1kIuVLSWGYxo1zmdq1f2WePOFn0K1cLq9U+YcPHzLVqlVj5s2bx1FE3KLBjFVDYWGhVuqlwYwscNHlUFhYWGL+rq55e3urrPJFKoemR2quqLuhsNAcUVFzeBuTUNl589QFQfRBZfYz4UqVThS46nJ4+fIlevfuTVtCkyqPrzEJ2kJdEIRU8UThwIEDCAsLw65duyq1sJK9vb1yoxB98PbtW3z33Xc0ZoHolEQCtG79M3Jzn+lVknDmzBmVrX/ZKJoF8ezZM/z8888cR0aIMFTZRCE/Px/Lly/H0KFDK7WXgz6ytLREixYtkJ2dzXcogrVu3Tq+QxAUiQTo1k0GhcIKV6/+R2+SBADw8PCoVGufs7MzZsyYgZ9++qnUvQQIMXRVNlHYvn07JBIJVq1apXEdaWlpHEbErS+++AK1atXiOwzBKtqNjpSvqLuhoMAYERET9W6dBFNTUwwdOrRSdfzf//0fFAoFJ7OiCBGaKpkoZGVlYdWqVfD29kazZs00quPvv//G4sWLOY6M6IuVK1fyHYIgGNqYBHXq1q2L+fPnY9u2bUhKSuI7HEJ0qkomChs2bEBubi5WrFihcR0uLi749ddfuQtKi1JTU7Fw4UIas0A4JZEAn366HtnZ/wgmScjNzdW4S+6bb75BrVq1KvXcIESIqlyi8PLlS/zyyy+YPXs27OzsNK7H1NRUME37DRo0QKdOnbS6/wSpWt6PSWAgEjXG9estBZEkAO9bAr/99luNylpYWOC7777Dvn37St06mBBDJWKq2NfMr776CgcPHkR8fDysra35DofoqfT0dNSpU4fvMPSS0LsbXr16hbp162pUViqVwtnZGa1bt8bJkyc5joyd6OhouLm54eDBg2jevDmvsRDhefjwIcaMGYOoqCi4urqWfbFWlnzSU/Hx8YyJiQmzZs0ajes4deoUhxERfeXp6cl3CHopJYVhmjRhGAcHRitbRQvBgQMHGABMeHg4r3EkJiYy5ubmDAD6Q380+mNubl6hVWirVIvCmDFjEBwcjCdPnsDc3Jx1+fj4eOzatQurV6/WQnS6ExcXh+3bt+OXX36hRaLUiI6OLj/LrmLej0lYByOjDrhxo6vgWhK4IpfL8dlnn8HKygpXrlzh9TOUlJREUzaJxurUqVOhVWirTKJw9+5dfPbZZ9i+fXupW3VWNSEhIejatWull7klVUNRd8Pbt8EID/+v3k2B1MStW7fg7OwMS0tL1mXPnj2LAQMG4Ny5c+jbt68WoiNEf1SZRKFfv3548uQJ7t+/DxMTE77DIUQwhD4mQZ1Lly7h4cOHmD17NuuyDMOga9euyMrKQnR0NCXcxKBViUQhNDQU3bp1w19//YURI0bwHY5eYhiGuiFICUWzGwoKRAaVJBSpzPs+PDwcHTt2xKFDh/Dll19yHBkh+sPg02CGYbB48WK4ublh2LBhGtXxxx9/ICsri+PI9EdERATmzp1L6ywUs2vXLr5D4F3ROgmZmacMMkkAUKnk2N3dHV5eXvjuu+9o6jExaAafKAQGBuLmzZtYu3atRs2DCoUCiYmJglkzQRNt27bFhAkTqEWhmOjoaL5D4FVRd4OJSS/cvDnIIJMELqxevRpPnz7Fnj17+A6FEK0x+K6Hvn37Ij09HREREXyHQoggGOqYhLIcOHAAY8eO1ajskCFD8PjxY/zzzz+UbBODZNAtCvHx8Th//jxmzpzJdyiCIpfLqRuiiiraBbIqJQkA8PjxY6SmpmpU1sfHBzExMbh+/TrHURGiHwy6RWHBggXYtWsXJBIJqlevznc4ghEUFISzZ89i48aNfIdCdEgiAVq3/hkKxUeIiJhQZZKEylIoFGjevDlcXV3h6+vLdziEcM5gWxTevXuH3bt3Y+LEiRolCY8fP8ahQ4e0EJn+69mzJ7766iu+wyA6VNTdYGo6GLdvj6ckgQWxWIwZM2bg+PHjePHiBd/hEMI5g00U/Pz8kJGRgenTp2tU/sGDB1V6Zb5GVfw3hZeXF98h6EzxMQnXrjUyiMWUdG38+PEwNjam2TLEIBls10P79u1hZWWF8+fP8x2K4OXn56NatWpVaqDWxYsX4eHhwXcYWieRAF27vkNhYfUqNSZBnYiICJiZmaFly5asy06ePBkXL15EQkICjI2NtRAdIfwwyBaFyMhI3L59Gz4+PnyHYhACAwOxZMkSvsPQqaqSJHz22RZkZPxJScL/1K1bF+fOndOorI+PD5KTk3H27FmOoyKEXwbZojBp0iQEBQUhISEBRkZGfIdjENLS0lCvXj2+wyAcKepuyMtLQ2hoXepu4EiHDh1gaWmJCxcu8B0KIZwxuBaFN2/e4PDhw5g2bZpGScLevXs1niZlyChJMBzFxyRcvVqPkgQO+fj44OLFi3j8+DHfoRDCGYNLFPbu3Qu5XI5JkyZpVD4xMRE2NjYcR2VYMjMzDX6dhVOnTvEdglZIJECXLm+q3DoJujJixAh89NFH2LFjB9+hEMIZg0oUFAoFtm/fjuHDh2v8y3758uW0E1w5zp49i5UrV/IdhlYZ4nx4iQRwdf0TGRk7KUkoR2ZmJoKCgliXMzMzw6RJk7Bnzx7k5eVpITJCdM+gxihcunQJHh4euH79Ojp27Mh3OAYtOzsbFhYWfIdBKqiou+Hdu2xcuVKTuhvKIZPJMHHiROzfv5912YSEBDg5OWHXrl3w9vbWQnSE6JZBJQqDBw9GQkIC7ty5U6Wm8hFSlqq4dwPf+vfvj7S0NNpjhhgEg2ljT01Nhb+/P2bMmKFRknDo0CEUFhZqITLDJ5FIDH7MglBJJEDnzhJKEnTMx8cHkZGRVX4XUmIYDCZRCAgIgEgkwogRI1iXZRgG165dg4mJiRYiM3wXLlzAhg0b+A6DfEAiAdq08UVGxi5KEnSsd+/esLKyMthBsaRqMZiuhwEDBiAnJwdXrlzhO5QqqaCgAKampnyHwRlvb2/s2bOH7zA0VtTdkJ9fgJAQExqToKGCggI8ePAArVu3Zl12zJgxiImJwZ07d7QQGSG6YxAtCrm5uQgKCqpS6/PrG0NKEgBhr8xYfEzClSumlCRUgpGRERYvXqxRWS8vL9y9exeJiYkcR0WIbhlEonDp0iVIpVJ4enryHQoBEBsbK/gxC1988QXfIWhEIgE6doylMQkcMTIy0rj7oHfv3jAxMUFAQADHURGiWwaRKPj7+6N58+Zo0qQJ67LR0dGQSqVaiKrqCg0NxR9//MF3GFWORAK0a3cWb94coiSBQ2ZmZhqVs7S0RLdu3eDv789xRIToluDHKMjlcjRo0ADe3t5Yt24d6/L9+/eHv78/7QnBMYVCQQtX6dC/YxIUCAkRUXeDntiyZQvmzZuH9PR01KpVi+9wCNGI4J/kt2/fxqtXrzQen3DixAlKErRA6EnC9evX+Q6hwlTHJIgpSdAChmGQk5PDupynpycKCwtpkygiaMJ+muN9t0OdOnXQoUMHjcpXq1aN44jIh27evCm4MQvr16/nO4QKkUiADh1u0JgELUtOTsbcuXNZl3N0dESrVq2o+4EImkEkCgMGDKBWAT32999/4+jRo3yHwcqRI0f4DqFc75OEMGRlnaEkQcscHBwwc+ZMjcp6eXnh7NmzkMlkHEdFiG4IeozCkydP0KRJE5w4cQKDBw9mVVYqlcLExETwTeRCwTAMLavNoeLdDcHBDHU36LGIiAi0a9cOV65cQdeuXfkOhxDWBP1bMiAgAKampujVqxfrslu2bEFwcLAWoiKloSSBOx/u3UBJgn5zc3ND/fr1qfuBCJagEwV/f3/06NEDNWvWZF22e/fu6Ny5sxaiIuUJDAwU3JgFffF+CmTg/2Y3UHeDEIjFYnh6esLf35/e90SQBJsovHnzBteuXdN4toOrqysNZOTJ06dPcfnyZb7DKNOCBQv4DqEEiQRwd7+PnJxwhISIKEngwe7duxETE8O6nJeXF548eYJHjx5pISpCtMuY7wA0FRgYCLlcjgEDBvAdCmHJx8eH7xDK5eDgwHcIKoq6GwAX/P33D5Qk8KR169bIzs5mXa5Hjx6oXr06/P394ezsrIXICNEewQ5mnDJlCm7evIl79+7xHQohWvXhmARKEoSpX79+YBgGgYGBfIdCCCuC7XqIiopC27ZtWZdjGAbLly/XQkREEwzD4NChQ9R3q8b7raL/+t8ukJQkCFmbNm0QFRVF73UiOIJMFPLz83Hv3j24ubmxLvv27Vs0aNBAC1ERTYhEImRlZSE6OprvUPSORAJ06pSMd+9iERJiQkmCwLm5ueHVq1dITk7mOxRCWBFkonDv3j3IZDK0adOGddnatWtj+vTpWoiKaGrGjBkaJX3aFBsby+v9i7obFIqGiI5eTlMg9Uh+fr5GU6uLnldRUVFch0SIVgkyUYiKioKRkRFatWrFdyjEQC1cuJC3e9OYBP1mamqK3377jXU5W1tb2NjYUKJABEewiYKLiwuqV6/OdyiEY3K5HFu3buW9H3fr1q283FciAVxdd+HduxxKEvSUWCzWaElykUgENzc3ShSI4Ag2UdCkqfr169eIi4vTQkSEK0ZGRjA1NUV8fDyvcfAxPVIiAbp0yYBU+gpXrtSgJEGPabrSaFGiwHciTAgbgksUpFIpYmJiNEoUzp8/j4iICC1ERbg0depUODk58R2GThV1N8hk1oiOXkxjEgxU0YDGlJQUvkMhpMIEt+DSvXv3UFhYqFGiMHLkSCgUCi1ERYjmaEyCMMnlcta71hY9t6KiotCwYUNthEUI5wTXolA0kPHTTz9lXdbY2BimpqZaiIpoS35+PtauXavzptp169bp5D4SCfDZZ1uRl/eKkgSBYbtjLQDY2dnRgEYiOIJLFCIjI2kgYxViZmYGGxsbpKWl6fS+eXl5Wr+HRAJ07ZoHmUyB0NA6lCQIzNy5cyGXy1mVKRrQGBkZqaWoCOGe4JZwdnV1RevWrbF7926+QyFEY9TdUHUtW7YMO3bswMuXL2n7dSIIgmpRqMxARl9fX1y6dEkLURHCDiUJVRsNaCRCI6hEoTIDGRs0aAAXFxctREV0KTMzE8uWLRPs9DKJBGjd+hfk5j6lJKGKKj6gkRAhEFSiUJmBjN26dYOtra0WoiK6VLt2bbRo0QI5OTlavU96ejrndUokQLduMigUtXH1qiMlCQZg3759rMvQgEYiNIJKFOLi4tCoUSMayFjFjRo1ChYWFlq9x8SJEzmtr6i7oaDAGBERE2mdBANx8+ZN1lOuRSIRXFxcaPE3IhiCShRSUlJo7jHRiRUrVnBWF41JMFzbt2+HWMz+MWpvb09jFIhgCC5RsLOzY11OIpEgJiZGCxERvqWmpmLBggWcj1lwdXXlpB6JBPj003XIzr5LSQJRsrOzo0SBCIagEgWJRAJ7e3vW5cLDw3H37l0tRET41qBBA3Tp0gWFhYV8h1LC+zEJDEQiJ1y/3oqSBKJkb2+P58+f00qxRBAEs4SzQqHQOFEYPny4YEfJk/J5enryHUIJ/45JEOHWraGUJBiwgoIC1iu+2tvbQyaTIS0tDfXr19dSZIRwQzAtCq9evYJMJtOo6wHQfLc3UjXt2rVL47I0JqHqkMlkGDFiBOtyRc8xiUTCdUiEcE4wiUJRf54mLQqk6oiLi8PcuXMr3YIUHR2tUbn3YxLW4u3bK5QkVAHGxsb45ptvWJcreo7ROAUiBIJJFIoyb01bFEjV0LRpUwwaNKjSicK2bdtYlylqSTAyao/w8K6UJFQRXbp0YV2mbt26MDExoRYFIgiCSRRSUlJgbGyMevXqsS47adIkLURE9FW3bt00mrJWGcW7G27c+C+tk0DKJBaLYWtrSy0KRBAEM5hRIpHAzs6O9S8AhUKBXr16aSkqou+KWha0OUalaHZDQYGIuhtIhdnb21OLAhEEQbUoaNLtIBaLMWrUKC1ERIQgIiKCkzEL6rwfk7AemZmnKEmoom7cuIH4+HjW5WgtBSIUgkkUUlNTaa8Gwlq7du3g7e3NukXBy8ur3GuKuhtMTHrh5s1BlCRUUcnJyXjy5Anrcra2tkhNTdVCRIRwSy8ThYULFyItLU3lWFZWFiwtLXmKiAhZ69atWZeZNWtWmeeLj0kIC/uMxiRUYSNGjEDv3r1Zl7O0tERWVhZncZT23CSEC3qZKAwaNAi///67yrHs7GzUrFmTdV1PnjzB8+fPuQqNCJxcLq9QN4SHh4fac0W7QNI6CaQyatasiezsbM7qK+25SQgX9DJRcHd3x61bt1SWN83JydFox8Bz587hwYMHXIZHBCw4OBjz5s3TuLxEArRu/TMyMg5QkkAqxcLCAjk5OZyNnyntuUkIF/QyUQCAgQMH4uTJk8qfs7OzNUoUZsyYgW7dunEYGRGyXr16ldutoE5Rd4Op6WDcvj2BkgRSKRYWFlAoFHj37h1ndX743CSEC3qbKIwePRoHDx4E8H6Km6aJgomJCYyNBTMLlOhAowr8hj916pTKz8XHJFy71ojGJBClnJwcjB8/nnW5oucZl90PxZ+bhHBFJ4nC3LlzSxxbs2YN5s+fjxUrVmD8+PElPizm5uZwdHREbGwsCgoKIJPJNBqjQEhZ8vPzS2369fX1Vf5dIgG6dn1HYxJIqUxMTDBw4EDWO5gWPc9ycnLUXvPhs5PNc5MQrugkUfhwZO+2bdtw9epVbNiwAStWrEDz5s0xduzYEuWmT5+Obdu2KT8MmrQoEFKWwMBALFmypMTxv/76C8D7JOGzz7YgI+NPShKIiqSkJPgdOYJ1Cxbgn/PnsWbePPgdOYKkpKQKla9Ii0LxZyfb5yYhXOGl62H9+vUqTXXjxo2Dv79/ibnIzZo1w/Pnz5GRkQEAMDMzY32vb7/9Frm5uZULmBiswYMHq93U598xCSMRETGLkgSiFBERgT1r1uCVnx888vLwhakpPPLy8MrPD3vWrEFkZGS5dVSvXh0AyhyjULy1i+1zk557hCs6TxQeP36M5ORktGjRQnnM1tYWlpaWCAkJKXH92LFjcfToUQCAkZER6/s5OjrCxMRE84CJwStt/5DiYxKuXq1HYxKIUlJSEs7t3o12WVnwadkSHezt0axOHXSwt4dPy5Zol5WFs7t2lduyULQcfVmzHooWCouLi2P93Ny/f78mL4+QEnSeKMTHx0MkEqFWrVoqxy0sLEr9YHl5eSEoKAgANNroZ/LkyTA1NdUsWFLlZGZmIiWFQZcub2hMAinVzfBw1Hn5En2cnJS/yM/GxQF4/4u9j5MT6rx8iZvh4WXWU/Q8q8h0xoSEBNbPzYCAgAq9HkLKo/PpAG/evAEA1KhRQ+V4zZo1leeKK9plrejvhGjT/v1nsHjRLshkbxETdhgONQoge8l3VERfyGQyvI48C3dbI8iN0pXHd925hX5NP4YIJhCJRHCztsbF8HAUDh2qtkWz6Hkml8vLva8mz01HR0fEx09U2HsAACAASURBVMejcePGFX59hJRG54lCUffBh90IhYWFkMlkJa5XKBRITk4utS5vb294eHjgiy++UB67fv061q9fjyNHjsDc3Fx5fMGCBXBwcMBXX32lPBYbG4uFCxdi69atcHBwUB5ft24d8vLysHLlSuWx9PR0TJw4EStWrICrq6vy+K5duxAdHV1i8JCXlxdmzZqlssLfqVOn4OvrqxwoR69D/14HwxRAoYiDhWkaVsxyxbZRqsuGT9yfiaGfmaF/y3/HywQ/kuLP63k4PMlK5doFx7PQyt4YY9v/+7rvphRi3YUcbBlpiY9q/pv4rjmfDXNTEeZ0/3dmT8obORaeyMKKARZoavPvR3XntVykZMrxvee/3y7zChhMPpCJ2f+tgQ6N/m1BOx79DsFxBfQ6OH4djo2MUTQEcee1XBQYSSEXZ8JYURcAYGZkhEOnT6PDgAEq7zlfX19cvHgRe/bsUR6ryD4kmjw3ExISKEkgnBAxLJcF8/Pzw8mTJ9W+uRmGgUgkwpdffokBAwYAACZOnIjdu3cDAEJCQtCzZ0+8fPkSderUUZaztbXF2LFjsW7dOpX6Tp48iZiYGCxbtgxBQUHo0aMHqxf48OFDNGvWjFojSIXk5uaiugkw5ssR2L9tDd/hED0jk8mwZ+NGdMjPR8tiY1u+8LsAv2EjIcL71oObKSm4aG6OJT//rLZF4dGjR3B2dsa1a9fQqVOnUq8penZq8txMTU2Fj49PZV8yIexbFEaMGIERI0ZofMOPP/4YAFTe8AzDIDMzs9SFcPbv3481a9Zg2bJlGi1NunLlSuzevVvl2ywh6hQ17R4+dpbnSIg+MgbwUZv+CPfzQ+uP6ii/MB0dNkZ5DcMwiMrIgHPPnmUOpC56nlXkS4wmz01aeIlwRedfsx0dHeHk5IRHjx4pj8XGxkIqlaJ79+4q1z569AgNGzZULkxSkb68D23cuFGjaZWk6khMTCzzfFJSEmfr8RPh6+DujnQbG5x/8qTE+4JhGJx/8gTpNjbo4O5eZj1FiUJZXQ9F9Wvy3PxwPAMhmuKlPX7cuHEqU3f27t0LLy8vNGnSROW67du3w8fHR/mLXpM10Rs0aEDdDkSto0ePqvQXl+bixYv49ddfdRQR0XcODg7oP2kSbteqhd/u3cPNlBQ8Sk/HzZQU/HbvHm7XqoX+kyapjLMpTV5eHoB/11MoTfEkgu1zkxCu8LIJwqJFi7BkyRLMmTMHlpaWePHiBfbu3atyTW5uLpKTk+Hs7AypVAqg7KVOCdHEoEGDMGzYsDKvmTx5MuvleYlha9OmDerVq4eb4eG4GB4OhVQKsbk5nHv2hKe7e7lJAvDv86yiK86yfW4SwhVeEgVjY2P89NNPZV5z8OBBjBnzvt+vWrVqMDEx4XTzFEIAqO1DHjlypMpsCFq0i3zIwcEBDg4OeN2rF7799ltsLmPgYmnYLk3P9rlJCFf0tk3+9OnTGDhwoPJnCwsLjRKF48eP4+HDh1yGRgTu3r175V5TfIrnh2JiYmjMAlGqVq0a+vbtyzqZ1MYeNh8+Nwnhgk4SBbYP1WvXrqFjx44qYwtq1qypUaJgbGyMgoIC1uWIYbpw4UKJ9R9KM2jQILXnrl+/Xu64BlJ11KxZE15eXqzLZWdnQywWlznYms2zs7TnJiFc0EnXg6WlZfkXFXPmzBnMnz9f5ZiFhYVGYxQouybFeXh4qCyAo4np06dTiwKptJycHFhYWJQ564HNs7O05yYhXGC94BJfPv/8c7Ro0QK7du3iOxRCCKm05cuXY/fu3WpXniVEXwimjapWrVp4+/Yt32EQAbp69SrrFoCLFy9W+Npr165RC0MV9vjxY6SmprIu9/bt2xKbPBGijwSTKNja2uL58+esy8nlco0+xMQw3L59GxcuXGBdbuvWrRW+9t69ezh16hTrexDDcOLECcTHx7Mu9/z5c+WGd4ToM8F0PXz77bfYv39/uXu8fygvLw/e3t4VGsBGCCFsFRYWQiQSwdiY3ZAvd3d3NG3atMRaCIToG8G0KNjb2yM1NZX1Ms7m5uZYtmyZlqIihFR1JiYmrJMEAJBIJLC3t9dCRIRwSzCJgp2dHWQyGdLS0liXdXFx0UJERF8FBARotC8IV06fPk1jFkiZ5HI5nj9/Djs7O75DIaRcgkkUijLvlJQUniMh+iwuLg4RERG8ziWXSCS4evUqb/cn+i8tLQ0ymYxaFIggCCZRKMq8JRIJz5EQfda0aVN8//33Zc5Nr4iZM2dqXNbHxwddu3at1P2JMBQWFuLrr79mXa7oOUYtCkQIBJMo1KlTB6amphq1KFy8eBExMTFaiIoYKldXV75DIAKQn5+P9u3bsy5X9ByjFgUiBIJJFMRiMWxtbTVqUWAYBunp6VqIiuiDQ4cOKXcY5cqkSZM4qYdhGOzZs4fGLBgoCwsLjBo1inU5iUQCExMT1KlTRwtREcItXnaP1JS9vb1GLQq9e/fWQjREH6SmpiIhIQGmpqZ8h1IqkUgEqVSKe/fuoVWrVnyHQ/RESkoK7OzsaF8GIgiCWUcBeL+j34sXLxASEsJ3KIQQorGxY8fi2bNnuHbtGt+hEFIuQaWzdnZ2NOuB6ER0dDTfIRABuHHjhkbliloUCBECQSUKzs7OSEhIQG5uLuuyaWlpvM6tJ9zZuXMnsrKytHqPFStWaKVemUyGTZs20ZgFA7Fq1SrWZRiGQUxMDJydnbUQESHcE1Si4ObmBoVCgbt377Iuu27dOjx+/FgLURFdyszMxNu3b2FhYaHV++zevVsr9RobG8Pc3ByJiYlaqZ/olp+fH+syycnJSE9Ph5ubmxYiIoR7ghqjUFBQAAsLC/z000+YPXs2q7JJSUmoXbs27dZGCOHViRMnMHToUEgkEtoUigiCoGY9mJqaolWrVoiKimJd1sHBQQsREUIIO1FRUahfvz4lCUQwBNX1ALzvftAkUSDCtXnzZrx48YLvMLQiLy8Pq1atojELVUhUVBR1OxBBEWSi8PDhQ40GNBLhyc/Ph5GREWxsbHR63+XLl+vkPubm5rC3t8fr1691cj/CnSlTprAuwzAMJQpEcASZKGg6oPHgwYN49uwZ90ERrTEzM8PMmTMrvXcDW+bm5jq71/jx42mFPoFhGAZdunRhXY4GMhIhElyi8Mknn8DU1BSRkZGsy9arV0+jbapJ1bNo0SK+QyB6TCQSYezYsazLFT232rRpw3VIhGiN4BKFygxo9PDwQLt27bQQFeHShg0b8OTJE77D4EVGRgaWLl1KYxYMFA1kJEIkuEQBoAGNhkwul8PGxgaNGzfmOxReWFtb47PPPkNeXh7foRAtoPEJRIgEmyjQgEbDZGRkhLFjx+p8TMKHkpKSeLv38OHDUaNGDd7uT8oml8sREBDAuhwNZCRCJdhEQdMBjRkZGXj69KkWoiKGZNasWXyHQPTU48ePNRojRQMZiVAJMlEoGtCoSffD69ev8fPPP2shKqKpdevW6V1X0vr16/kOAcD7Xy7z58+nMQt6xNnZWaO9QIre45QoEKERZKJgamqKli1bapTVOzk5YfXq1VqIimiCYRg0b94crq6ufIeiQl827GnYsCG6d+8OmUzGdyikGE26xiIjI2FjY0MDGYngCGqvh+KmT5+Oq1ev4sGDB3yHQggh5fLw8ICJiQnOnj3LdyiEsCLIFgUA6N69Ox4+fEi78BFCdCYnJwcKhYJ1udzcXFy9ehU9evTQQlSEaJdgE4XevXvDxMREo9HHAKjPl0fr1q3DpUuX+A6jTFu2bOE7hFLdv38fc+bMofcvT5YuXYq4uDjW5S5dugSpVApPT08tREWIdgk2UbC0tES3bt3g7++vUflx48YhPz+f46hIRbi7u6Nnz558h1EmPqdHlsXFxQXDhw/nO4wqa8KECWjWrBnrcv7+/mjevDmaNGmihagI0S7BjlEAgK1bt+Kbb77Bq1evYGn5/+3deVxUVf8H8A+bIIuZmGaKW5oLSKkYLrgmrjCQS+6Wigv4mNpTpvhU9uReWmoupIkS7hqyCaKoKaAkGG4ouYUguCEo2yPMzP39YfCTFIWZO3Nn+bxfL1/FOPecD7648OWcc895pVrXxsXFwdHREa+++qqG0hERPdl3oUGDBpg4cSKWLl0qdRyiatPbEQUA8PT0RGlpKQ4ePFjta93c3FgkaJEe16M6TRAE/tvquMTERNy7d4/TDqS39LpQaNKkCZydnVWefiDtWL58Ofbs2SN1DIN08uRJzJo1S+oY9AJhYWGoW7cuOnfuLHUUIpWYSx1AXTKZDGvXroVcLoe5ud5/OgZp0KBBcHR0lDpGtRQVFWn1qGlVde3aFbVq1ZI6hsG7cuUKDh48qNKOneHh4fDw8ICZmZkGkhFpnl6PKABPCoXc3FzEx8dX+9ri4mKdXd1uSJycnCQ/u6G6Ro4cKXWEKnNycpI6gsHLy8tTaUTg6tWrSE1NhUwm00AqIu3Q+0KhY8eOaNCggUrTDzVr1sS9e/c0kIpKS0uljqCWOXPmSB1BJXK5nGsWNKBTp05wcXGp9nXh4eGwtLSEu7u7BlIRaYdeP/VQZurUqYiNjcWVK1f07jdXQ7Ry5UrUqlULPj4+UkcxOlFRUTh8+DDPM9ERvXv3hrW1NXdjJL1mEIVCZGQkPDw8kJqaijZt2kgdx+jdvHkTDg4OLNokcvPmTTRu3FjqGEbvwYMHqFevHtauXYupU6dKHYdIZXo/9QA82c7Z2tqaTz/oiMaNG7NIkBCLBPHI5XJs2bJFpWujoqKgUCjg4eEhbigiLTOIQqFmzZro16+fyts55+bmIi4uTuRUxqWwsFDqCKLasWOH1BFEUVRUxDULakhNTUVJSYlK14aHh8PFxQUNGzYUORWRdhlEoQA82XwpISFBpcWJ1tbW2LBhgwZSGYd169Zh48aNUscQVUxMjNQRRBEZGYn58+dLHUNvOTs7Y8qUKdW+rqSkBFFRUdxkiQyCQaxRAIC7d++iYcOGWLFiBT7++ONqXy8IAofLVZSTk4M6derw309H5eTkwN7eXuoYRiUkJARDhgzBuXPn0K5dO6njEKnFYAoFABgxYgTOnTuH1NRU/tAiIsn07dsXxcXFKu3vQqRrDGbqAQD8/Pxw+fJlHD16VOooBu/+/ftSRyAV5OTkcM1CFZSWluLIkSMqXXv58mXExsbCz89P5FRE0jCoQqFHjx5o27Yt1q1bp9L1paWlOH/+vMipDE9gYCB++uknqWOQCiIjI7Fo0SKpY+i8o0eP4tKlSypdu2HDBtStWxfDhg0TORWRNAxq6gEA1q5di5kzZyI9Pb3aq40VCgUGDRqE6OhoTl28QFFREWrWrGnQ/0YjRozArl27pI6hEfpyjoXUlEolTE2r97tUYWEhGjZsCF9fXyxZskRDyYi0y6BGFABg3LhxsLKyUmkVvpmZGfbv32/QPwDFYG1tbfD/RqNGjZI6gsawSKia6hYJwJPHah89esQNlsigGNyIAgD4+voiNDQU6enpsLCwkDqOQUhPT0eTJk2kjkEiS09P5wZZIhEEAR06dECjRo1U3tOFSBcZ3IgC8KRQyM7ORmhoqNRRDMKePXsQGBgodQzSgEOHDuGHH36QOobOyMzMREZGhkrXJiYmIiUlhYsYyeAY5IgCAHTv3h0WFhZqrVxu3bq1yKn0k1wuh5mZGX/rNFByuRzm5uZSx9AJs2fPxqRJk1Q6unv8+PGIi4vD1atXVZq2INJVBvvV7Ofnp9bK5dWrV+PChQsip9JP5ubmRlckGMrOjFXBIuH/LV++XKUi4f79+9i1axd8fX1ZJJDBMdiv6CFDhqBevXpYv369StcvW7YMbdu2FTmV/jD2x0R//PFHqSNI4vz580a9z4Kqa5o2b94MExMTTJgwQeRERNIz2ELB0tISPj4+2Lp1KwoKCqp9vZ2dndH+ZhATE2OwjwZWlbGeRBofH6/yaYnGSqFQYMOGDRgxYgTq1q0rdRwi0RnsGgXgyYru5s2bY/369Sod7GKsyr4kjG26gZ4wxnNPTpw4ATc3N5U+7wMHDmDw4ME4deoUXF1dNZCOSFoGXSgAgJeXF/766y+kpKSo9E3g4cOHePDgAZo1a6aBdEQktZycHMyYMQPbt29X6XoPDw9kZ2cjKSnJ6AosMg4GP7Y+Y8YMnDt3DpGRkSpdX1xcjLlz54qcSvccP37cqOem6fmM4evC3t4ev/zyi0rXnjlzBpGRkZgxYwaLBDJYBl8ovPfee+jVqxfmzZsHhUJR7etff/11bN26VQPJdMfp06dx8OBBqWPolOnTp0sdQSdcuHDBKPYjMTMzU+k6f39/tGrVCmPHjhU5EZHuMPipBwA4deoUunTpgqCgIIwbN07qOKQHfv75Z0yaNEnqGKTDjh49ij59+mDv3r0YOnSo1HGINMYoCgXgyeOSZ86cQVpaGiwtLaWOQ0QSS0hIQOPGjdGoUaNqXysIAjp37gxBEJCYmMhpBzJoBj/1UGbRokXIyMhAQECAym0cP34cubm5IqaSTlhYmEpTMWTcQkNDDWbNQlBQEGrXrq3StSEhIfj999+xdOlSFglk8IymUGjTpg0++ugjLFy4EPn5+Sq3ExwcLGIqafz5559ISkoy2n0iSHW3bt3C8ePHpY4hig0bNsDW1rba18nlcvj7+6Nfv37o06ePBpIR6RajmXoAgIyMDLRs2RJz587FggULpI5DOuzMmTPo0KGD1DFIB23atAmTJ09GcnIyv0bIKBhVoQAAn376KQICAnDt2jXUq1dP6jiko2QymdHuzkiVKy4uRsuWLeHm5oadO3dKHYdIK4xu7HnevHkwNTXFokWLpI6iVdu2bcPjx4+ljqE3Nm/eLHUEnScIAgIDA/VqzUJMTIzKJ8oCT84AuXPnDhYuXChiKiLdZnSFgr29PebMmYP169fjxo0bKrezZs0aZGdni5hMc7Kzs3H9+nXUqFFD6ih6g3v2v5yJiQkeP36sV6es3rhxQ+VtlvPy8rBkyRL4+PigRYsWIicj0l1GN/UAAIWFhWjRogXc3d0RFBSkUhvnz59HdnY2+vXrJ3I6ItJF/v7+WLVqFa5evYoGDRpIHYdIa4yyUACA9evXY/r06UhJSYGzs7PUcYhIh2VlZaFFixaYPXu20U1bEhnd1EMZHx8fNG/eHP7+/lJH0YiAgAA8fPhQ6hh666uvvpI6gt6Ry+X44YcfdG7NwuPHj9XeM+S///0vrKys8Nlnn4mUikh/GG2hYGFhgYULFyIyMlLtcw4KCwt16pvjw4cP8ejRI9SqVUvqKHrL2tpa6gh6x9zcHDY2Nrh586bUUSqYO3cuEhISVL7+7Nmz2LRpE/z9/VXeoIlInxnt1APwZNV2v379cPnyZVy4cAGvvPKKSu2sWrUKtWvXxocffihyQiJS19WrV1VefFhaWop3330XCoUCSUlJXBBMRsmoCwUASE9Ph5OTE0aOHImNGzeq1IZCoUBWVhYcHBxETkdEUvr666/xzTffIDExER07dpQ6DpEkjHbqoUyTJk3w3XffYdOmTSpPQZiZmUleJKxevRq3b9+WNAPR04qKirBw4UKdmparjrNnz2LhwoWYN28eiwQyakZfKADAlClT0LdvX/j4+OjlAsD//e9/MDc3R/369aWOYjB0bZ5dH1lbW6Nx48bIycnRet/79u3DgwcPVL6+tLQUH330Edq0aYMvvvhCxGRE+oeFAp5sHLNp0ybk5eXh008/VautS5cu4dChQyIlqxorKyv4+fnxFDsR/etf/5I6gkEYP3681jevKi0tRXx8vFoLDxcvXozz588jMDCQ6xLI6LFQ+JsYUxAA0KxZM5w4cULEZCSF5cuXSx2BVGRhYYGVK1eqfDoqpxyIKjL6xYxPE+spCG1YsWIFZDIZWrZsKXUUoirJycnBypUrsXDhQp0d/eJTDkTP4ojCU8ScgtAkhUKBevXqcb950iv29vZ45513UFRUpJH21VmTUKZsymHLli0sEoj+xhGF5wgICMC0adMQHR2N/v37q9VWRkaG5E9EEBm6Q4cOISIiAqtWrVK5jbNnz8LFxQVz587FN998I2I6Iv3GQuE5xJyCGD16NPz9/eHk5CRiQtK0NWvWYMaMGVLHoCoqLCyEubk5LC0tVbqeUw5ElePUw3OUTUE8fPhQ7SmIzZs3w9HRUe1My5YtQ1JSktrtUNXw8UjNy8jIwL///W9R9lmwsbFRuUgAOOVA9CIsFCrx9FMQ0dHRKrdjZWWl9sItQRDQtm1brsDWom+//VbqCAbPwcEBffv2hVwuV+l6sQZDU1JSsHDhQvj7+6NDhw6itElkSDj18AKCIGDgwIFITk5GcnIyGjdurHabCoUCZmZmIqQjMl5KpRKTJk3CkiVL8Prrr6vcTm5uLjp16gRbW1v8/vvvHE0geg6OKLyAiYkJgoODYWtrC29vb7VXa1+8eBGTJk3S2y1tiXSFUqnExIkT1SoSFAoFRo4cidzcXPz6668sEogqwULhJerWrYv9+/cjLS0NkydPVuuHvKOjI+bMmVOlqYilS5ciJiZG5b5IPZp6hI8qd/HiRcycObNK95i5uTm6d++uVn/+/v44fPgwdu3ahebNm6vVFpEhY6FQBW+//TYCAwOxfft2rFy5Uq222rZtW6X3ubm5wd3dXa2+SHUjR46UOoLRcXR0xAcffKCVvnbu3Inly5fju+++Q9++fbXSJ5G+4hqFapg3bx6WL1+O6OhoUX6IC4KgszvUGbu4uDi4ublJHYOesn//fpiYmMDLy0utdlJSUtC1a1cMHToUQUFBvAeJXoKFQjUoFAp4eHggMTERSUlJag9Xbtq0CTVr1sSYMWMAsHAgelrZt6aye2Lv3r3w8vKChYWFym3ev38fLi4usLe3R1xcHGrWrClKViJDxkKhmnJzc/Huu+/CysoKJ0+ehK2trcptlW3u4urqim+//RaNGzfGiBEjRExLpL/i4+Oxe/dutXZbfFppaSn69++PCxcuICkpSZSnmIiMAQsFFaSmpsLV1RX9+/fHnj17RBkFuHDhAhwdHTmiQPSUixcvirJhGQDMmjULa9euRWxsLHr06CFKm0TGgIsZVdC2bVv88ssv2LdvHxYtWiRKm05OTnxsUofs2LFD6ghGLzY2FnFxcaK0tWXLFqxatQqrVq1ikUBUTSwUVOTt7Y2vv/4aX3zxBbZu3apSG6WlpRU+XrFiBX755Rcx4pGa+Giq9JRKJcaPH1/+cWlpqUrF9MGDBzF58mRMnjwZvr6+YkYkMgqcelCDIAiYOnUqNm/ejNDQUAwePLjK137//fewtbXF5MmTy19TKpW4fv06j48meo6oqCjExsbiu+++q/I1v//+O/r06YPevXsjJCQE5ubmGkxIZJhYKKhJLpdj2LBhiImJwZEjR9C5c+cqXXfz5k04ODhwTQLRU162xXl1jm1PS0uDm5sbWrZsicOHD8Pa2lqsmERGhYWCCIqLi9GvXz+kpqYiLi4Obdq0EaXdu3fvwt7enmdDkFFYsWIFateujUmTJqndVlZWFrp27Qpra2vExcWhTp06IiQkMk4sFESSm5uLHj164OHDh0hISECjRo2eeU9hYSFsbGyq3GZYWBiOHTum9m6QRPogPT0djRs3rvIoW2FhIaytrZ95f15eHnr06IHc3FwkJCRUeQSCiJ6PhYKIbt26ha5du8LW1hbHjh3Da6+9Vv53a9euRUlJCWbPnl2tNktLS9XaYIZUM2LECOzatUvqGPQCu3fvRkpKChYvXlz+WmFhIQYMGICLFy8iLi6uylumE1HlWCiILC0tDT179kT9+vVx5MgR2NvbAwBycnJQp04drknQE/v374e3t7fUMQxaRkYGLCws1DoBMicnp/weKyoqwuDBg5GUlISYmBh06dJFrKhERo2PR4qsVatWiI2NRXZ2Nvr27YsHDx4AAOzt7dUuElJTU7F//34xYtJLsEjQLEEQ8J///AfFxcVqtVNWJBQXF8PLywunT59GVFQUiwQiEbFQ0ABHR0fExsYiIyMD7u7u5cVCmTlz5uDu3bvVbrdFixZIS0uDQqEQKyqRJExMTLB161Y0a9ZM7bbKioT4+HhERkaKdpiXqvcpkaFhoaAh7dq1w5EjR3Dz5k289957uH//fvnfeXt7IyAgoNpt1qhRA59//jmfgiD6W1FRETw8PMqLhJ49e4rWtqr3KZGhYaGgQc7Ozjh69CiysrLQp0+f8t9OunbtisTERCiVSrX7yM3NVbsNehZ3ZhRXZmYmRowY8cxupOooKCjA4MGDkZiYiOjoaPTu3Vu0tgFx71MifcZCQcOcnJxw7Ngx3Lt3D926dcP169cBAF5eXggJCVGr7bKdIRMTE8WISk/58ccfpY5gUGxtbbFs2TLRnuC5e/cuevfujeTkZBw8eBDdu3cXpd1/EuM+JdJ3fOpBS27cuIF+/fohPz8f0dHReOuttzBmzBi1vwkplUoolUpuTUtG4+l7KSoqCu3bt9dYX0VFRaLcp0T6jCMKlZg1a5ao7TVr1gzx8fFwcHBAjx49kJiYiKZNm+Ly5ctqtWtqasoigXTOhQsXEBERIXq7Z8+eRdeuXQEACQkJaN++vej36tOsra1FuU+J9BkLhUo8evSoWu/fs2fPS99Tr1698vMgBgwYgKZNm2Lt2rWqRnyu0NBQLFiwQNQ2iarrxIkTcHFxEbXNY8eOoUePHmjYsCHi4+PRvHlzANW/V6tr2rRpot+nRPqEhYJIDhw4UKX32dnZISIiAkOHDsXs2bMRFxeHwsJC0XJ4eXlh5MiRorVHpApfX1+1NlL6p3379qF///5wdXXF0aNHUa9ePdHafplWrVohKytL1PuUSJ+wUBBJdTZTqlGjBoKDgzFz5kykpKRg8ODBoq4Gb926tWhtGavp06dLHUFvKJVK7N+/H5pY7qRUKvHNN99g9J4+dgAAD69JREFU2LBhGDp0KCIiImBnZyd6Py8zbtw4BAUFab1fIl3AQkEipqam+P7777F27VocP34c7u7uuHfvnkb6+uSTT/DHH39opG1D1aFDB6kj6I34+Hjcvn1b9Hbz8/MxfPhwfPnll/j6668RHByMGjVqiN5PVchkMoSHh0vSN5HUWChIzM/PD15eXjh//jxcXFxw5swZ0fuYP38+rK2tRW/XkIlx1LGx6N69O6ZNmybqOSbXrl1Dly5dcOjQIYSGhuLLL7+Eqal0365MTU3RtGlTXLt2TbIMRFJhoSASVYddlUoliouLkZKSgnr16qFbt27Yvn27qNns7e3RqlUrUdsk4xUREYGsrCyNtR8TEwMXFxeUlJQgMTERMplMY31VlVKpxPXr1/Hmm29KHYVI64ziubrdu3cjJCSk0t94BEGAiYkJRo8eDQ8Pjxe2JZfLMXz4cDx+/LjC9RcuXMCgQYMqvNaoUSNs3Ljxhe2FhoZCJpPBwcEBx48fx7Rp0zBmzBj88ccfWLJkiUYefczPz8e4ceOwbt06vPHGG6K3T4aroKAAKSkp6NOnj+htC4KAFStW4PPPP8eAAQOwbds21K5dW+X2xLzvy+5TIqMk0HNNmDBBo+8v4+3tLRQUFJR/rFQqhR9++EEwMzMT3N3dhZycHJXafZlbt24JxcXFGmnbECQnJ0sdwagUFhYKo0aNEgAI/v7+glwur/K1qt571fHP+5TImHDqQSSCClMPaWlpcHBwgI2NTflrJiYmmDlzJmJiYnDmzBl06tQJ58+fFzMqAOCNN96AlZVV+cclJSXIz88XvR99xb0o/v83/IMHD2q0n/T0dHTr1g2hoaHYvXs3Fi1apFMHnz3vPiUyJiwURKLKQq7169fDz8/vuX/Xp08fnD59GnZ2dnB1dcXq1as1ejhNZmYmhg8fjoKCAo31oU82b94sdQTJmZiY4N1334W7u7tG2hcEAdu2bUP79u3x8OFDnDx5EsOHD9dIX+p40X1KZAxYKIikuiMKhYWFyMjIeOGeB2XbPvv4+GDmzJno1asXrl69qm7U52revDmioqJga2urkfb1Td26daWOoHVyuRwPHjyo8Fr37t018rRBdnY2vL29MXbsWAwcOBBJSUlwdnYWvR91VeU+JTJ0LBREUt0RheDgYIwdO/al77OxscHq1atx7Ngx3Lp1C87OzhobXfjn55CSkoLVq1ejpKRE9L5I90yZMgVJSUka7aNsFMHR0RGJiYkICQnBtm3bUKdOHY32q6qq3qdEhoyFgkjmzJlTrfeHhobCy8uryu/v2bMnzp07h0mTJml8dKGMk5MTGjdurFPzxaQ5mzdvRr9+/TTW/j9HES5evAhvb2+N9SeG6t6nRIaIhUIlqjuVUJ2hyRMnTqBbt27VHtK1sbHBmjVrtDK6AADm5ubw9vauUCjk5eUhLS1NI/3pkq+++krqCBq1YMEC/Prrr1rpq7JRBHt7e9Ha1wRV71MiQ8M7oBKvvPKKxtqOiIjAlClTVL7+n6MLvXv31tqOcUVFRVi5ciUePnyolf6kYug7WY4ePRrvv/++xvvRxiiCpu5Vde9TIkNhImiqHCet+O233zBx4kTcvn0bS5cuxfTp07X+G5BSqcTt27e5eZMOKi0txfr16+Hq6gpXV1et9SsIArZv344ZM2agRo0a2LBhg85PMxDR83FEQc+VjS5MnDgRH3/8sVZHF8o8evQIn332GVJTU7XaL72cubk5WrZsifbt22utT31ci0BElWOhYACeXruQmZkJZ2dnLF++HMXFxVrpv3bt2ti2bRvatm1b4fVz585BoVBoJQMBd+7cwSeffIK7d++Wv2ZiYoKBAwdq5dRFuVyOn376SWNrEYhIGiwUDEjZ6MLkyZMxf/58vPXWW/j5558hl8slyRMVFYWwsDBJ+lbXzZs3pY5QbVZWVvjoo4/w2muvabVfQRCwd+9eODo6YurUqfDw8OAoApEB4RoFA3X16lV88cUX2LlzJ1q3bo1Fixbh/fffF/UoYFXs3bsXdnZ26N+/v6Q5XkYmk+l0kbN3715ERkYiMDBQ0hyxsbGYO3cukpKSMHDgQCxevBjvvPOOpJmISFwcUTBQLVq0wI4dO5CcnIwmTZpg6NCh6Ny5M44ePSpprs6dO8PCwqLCa3K5XKPbU6ti+fLlUkcod+nSpWfO+5DJZJIWCcnJyejXrx/69u0Lc3NzHDt2DAcOHGCRQGSAWCgYuA4dOiA6OhpHjhwB8OQMiQEDBuCPP/6QJE+jRo2eOaI4LS0NgwcPRm5uriSZnkeqLXuVSuUz+wLExMQ8szumNtYcPM+VK1cwYsQIuLi4IDMzEyEhIUhISEDPnj0lyUNEmsdCwUj07t0bp06dwr59+/DXX3+hQ4cOGDVqlNafkHgeR0dHREVF4dVXX63wuq+vLyIjIyVKpX2XLl2Cp6cn7ty5U+H1mTNnomPHjhKleiIrKwvTpk1DmzZtcPLkSWzevBnnzp2Dt7e35NNZRKRZXKNghORyObZs2YIFCxbgzp07mDJlCr744gu8/vrrUkeroKSkBAUFBRXOAYiJicHhw4exbNkyvf4BtXjxYpSWlur8DpB5eXlYtmwZVq1ahZo1a2L+/Pnw8/OrcEQ5ERk4gYxWUVGRsHz5cuHVV18VrK2thblz5woZGRlSx3qh0tJS4cqVK8+8PmrUKOHXX3+t8FpeXp6QnZ0tKJXKavezevXqal9z/fp14fz58xVeu3nzpjBo0CDh0qVLFV5XJZM23bt3T1i8eHH518b8+fOFvLw8qWMRkQRYKJCQm5srzJs3T7C1tRXMzMyEIUOGCIcPH9b5H2b/pFAoKnwcHx8vTJs27Zn3+fj4CMHBwRVeu3jxovDll18KhYWFgiAIwqeffioIgiAEBAQIu3btqvDetLQ0wdPTU7hx40aF13fs2CHs3btX3U9DMkqlUjh16pQwfvx4wdLSUrC0tBR8fX2FrKwsqaMRkYQ49UDlHj16hODgYKxbtw4XL15Eq1at4Ovriw8//BC1a9eWOp5oBEGAUql85rCrGzduoF27djA3Ny9//dq1a7CyskLDhg2liKoVRUVF2LFjB9atW4czZ86gWbNm8PX1xYQJE1C3bl2p4xGRxFgo0DMEQcCJEyewbt067Nu3DxYWFhgzZgz8/Py0uhUwaVZaWho2bNiAwMBAPHr0CIMHD4afnx/69+/PExOJqBwLBXqh27dvY9OmTQgICEBmZiY6d+4MPz8/DB8+nAva9JBcLkd4eDjWrVuHw4cPo27duvDx8cGUKVPQrFkzqeMRkQ5ioUBVIpfLERERgXXr1uHQoUOwt7fHpEmTMHXqVDRv3lzqeKIrKioyqKOms7Ozywu+W7duoUuXLvDz88OwYcNY8BHRC7FQoGr7888/y4esHz58CHd3dwwZMgQeHh4GM5ev61s4V8X9+/cRGRmJ/fv3IyIiAjVq1MCYMWPg6+vLKSQiqjIWCqSyoqIi7Ny5E0FBQYiLi4NCoYCLiws8PT0hk8nw9ttv6+1eB3FxcXBzc5M6RrWlpaUhLCwMYWFhSEhIgFKphKurK0aNGmVwi1KJSDtYKJAoHjx4UH5aZFRUFPLz8+Hg4ACZTAaZTIaePXvC0tJS6pgGRy6XIyEhAWFhYQgPD8eff/6JmjVrwt3dHZ6envDw8NC5jbSISL+wUCDRlZSU4LfffkN4eDjCwsKQnp4OOzs7DBgwADKZDAMHDoS9vb3UMfVWfn4+Dh48iLCwMERGRuLBgweoX79++UjOe++9Z1DrK4hIWiwUSKMEQcD58+fLh8NPnz4NU1NTuLm5QSaToUePHnB2duZowwuUlpYiNTUVcXFxCA8Px9GjR1FSUoJ27dpBJpPB09MTnTp14iONRKQRLBRIq7KzsxEREYGwsDAcPnwY//vf/2BhYQEnJyd07Nix/I/UxcOOHTswatQorfdbVhQkJycjOTkZSUlJOHv2LB4/fgxzc3P06tULnp6e8PT05OOMRKQVLBRIMsXFxTh37lz5D8Xk5GRcuHABCoUC5ubmaNeunWTFw4QJExAYGKjRPp4uCpKSkpCcnFxeFJiYmKB169bln7uLiwveeecd2NraajQTEdE/sVAgnfKy4sHJyQkuLi7o0KED3nzzTTRs2BCNGjVCrVq1dPYJi4KCAmRmZuLWrVu4ceMGzpw5w6KAiPQGCwXSeS8qHsrY2NigUaNG5YXDP//72muvwc7ODnZ2dhXOclCVQqFAfn4+CgoKcP/+/fJC4Hn/ffToUfl1LAqISN+wUCC9VFJSgqysrPIfxs/7AZ2VlQW5XP7MtZaWluVFg52dHWxtbWFhYQFTU9PyP0qlsvyPXC5HQUFBeWGQn5+P4uLiZ9o1NTVFgwYNXliwNGzYkDshEpFeYaFABkupVOLu3bvIzMxETk5OhR/0T/9/QUEBSktLKxQHTxcN5ubmsLW1ha2tbYXiouy/derUQaNGjVC/fn1RRiuIiHQJCwUiIiKqFB+8JiIiokqxUCAiIqJKsVAgUtGcOXNw9+5dqWMQEWkUCwUiFXl7eyMgIEDqGEREGsVCgUhFXbt2RWJiIpRKpdRRiIg0hoUCkRq8vLwQEhIidQwiIo1hoUCkhjFjxiA4OFjqGEREGsNCgehvs2bNeu7rsbGx6NWr13P/ztraGk2bNsXly5c1mIyISDrcRo7ob0+fyQAAe/bswYEDB1BQUICbN29Wet20adPw448/Ys2aNZqOSESkdRxRIKrE8OHDERgYCA8Pjxe+r1WrVsjKykJhYaGWkhERaQ8LBSIRjBs3DkFBQVLHICISHQsFIhHIZDKEh4dLHYOISHQsFIhEYGpqiqZNm+LatWtSRyEiEhULBSIRKJVKXL9+HW+++abUUYiIRMWnHsgg7d69GyEhITAxMXnu3wuCABMTE4wePfqlixWrIjQ0FDKZTO12iIh0DQsFMkgffPABPvjgA631FxQUxI2XiMggceqBSE1paWlwcHCAjY2N1FGIiETHQoHoJRQKxQsPflq/fj38/Py0mIiISHs49UBUiejoaGzatAlxcXG4d+8eunfvjtatW2Pjxo3l7yksLERGRgZat24tYVIiIs1hoUBUiQEDBmDAgAEvfE9wcDDGjh2rpURERNrHQoFIDaGhoYiIiJA6BhGRxnCNAtHfBEGo1vtPnDiBbt26wdSUtxERGS5+hyP62yuvvFKt90dERGDKlCkaSkNEpBtMhOr+GkVERERGgyMKREREVCkWCkRERFQpFgpERERUKRYKREREVCkWCkRERFQpFgpERERUKRYKREREVCkWCkRERFQpFgpERERUKRYKREREVCkWCkRERFQpFgpERERUqf8DVHjUaJgFrHIAAAAASUVORK5CYII=",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000025C21748>)"
      ]
     },
     "execution_count": 62,
     "metadata": {
      "comm_id": "e0f5e48c-a6c9-49fa-81d9-aea0615102a5",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U = tH                    # We entered tH as a default. \n",
    "                          # You could also input other real-valued unitaries, for example pX or pZ. \n",
    "\n",
    "unitary_transform_plot(U) # Note, complex valued state vectors are not supported     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\">edX Exercise 7</h3>\n",
    "\n",
    "Let's imagine that Alice wants to send a bit $x \\in \\{0,1\\}$ to Bob. Having gone all quantum, however, Alice has lost all means for classical communication. Unfortunately, Alice and Bob also have quite funny quantum devices.\n",
    "\n",
    "Concretely, Alice has a device that can only prepare the state $|+\\rangle$. Thankfully, however, she can apply one of two unitaries $U_0$ and $U_1$ of her choosing transforming her state to $|\\psi_x\\rangle = U_x |+\\rangle$. To be fair, we at least allow Alice some control over her circuit so that Alice can decide to apply $U_x$ depending on her input bit $x\\in\\{0,1\\}$. \n",
    "\n",
    "<img src=\"source/figure_exercise_7.svg\">\n",
    "\n",
    "Alice can now send her state $|\\psi_x \\rangle$ to Bob. Bob can only measure in the standard basis, and will take his measurement outcome $b \\in \\{0,1\\}$ to be the value of $x$. \n",
    "\n",
    "Your goal in this exercise is to come up with a protocol so that Alice can communicate $x$ to Bob, no matter whether $x=0$ or $x=1$. Concretely, your goal is to determine what transformations $U_0$ and $U_1$ she applies for the cases $x=0$, and $x=1$. \n",
    "\n",
    "In other words we ask you to find two unitaries $ U_0$ and $U_1$ that Alice can apply such that the probability that Bob obtains measurement outcome $B=x$ is given by\n",
    "\n",
    "$$ P(B=x) = \\big| \\langle x \\: \\lvert \\: U_x \\: \\rvert \\: + \\rangle \\big|^2 = 1 $$\n",
    "\n",
    "---\n",
    "\n",
    "You can check if you have found two such unitaries by making use of the code block just below.\n",
    "\n",
    "Enter $U_0$ and $U_1$ as is described and you will see the associated $p_0$ and $p_1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You entered U_0 =\n",
      "[1 0\n",
      " 0 1]\n",
      "For this case the probability of Bob's measurement outcomes are:\n",
      "p_0 = 0.5\n",
      "p_1 = 0.5\n",
      "\n",
      "\n",
      " You entered U_1 =\n",
      "[1 0\n",
      " 0 1]\n",
      "For this case the probability of Bob's measurement outcomes are:\n",
      "p_0 = 0.5\n",
      "p_1 = 0.5\n"
     ]
    }
   ],
   "source": [
    "## enter values for U_0 - as a default we have taken the identity matrix\n",
    "U_0 = [1 0;0 1];\n",
    "\n",
    "## enter the second unitary U_1 - as a default we have taken the identity matrix\n",
    "U_1 = [1 0;0 1];\n",
    "\n",
    "# Let's define the standard basis and the plus state\n",
    "v0 = [1; 0];\n",
    "v1 = [0; 1];\n",
    "plus = [1; 1]/sqrt(2);\n",
    "\n",
    "## let's compute the outcome probabilities if Alice applies U_0\n",
    "\n",
    "# first, let's compute the output vector by applying the unitary transformation\n",
    "outVec = U_0 * plus;\n",
    "\n",
    "# then the probability that Bob measures b = 0 is given by the absolute inner product squared:\n",
    "val = v0'*outVec;    \n",
    "p_0 = abs(val[1])^2; # take the square of the absolute value.\n",
    "\n",
    "# same for outcome b = 1\n",
    "val = v1'*outVec;\n",
    "p_1 = abs(val[1])^2;\n",
    "\n",
    "# for printing, let's round the outcomes\n",
    "digits = 3;\n",
    "p_0 = round(p_0, digits);\n",
    "p_1 = round(p_1, digits);\n",
    "\n",
    "println(\"You entered U_0 =\")\n",
    "println(U_0)\n",
    "println(\"For this case the probability of Bob's measurement outcomes are:\")\n",
    "println(\"p_0 = $p_0\")\n",
    "println(\"p_1 = $p_1\")\n",
    "\n",
    "## let's compute the outcome probabilities if Alice applies U_1\n",
    "\n",
    "# first, let's compute the output vector\n",
    "outVec = U_1 * plus;\n",
    "\n",
    "# then the probability that Bob measures b = 0\n",
    "val = v0'*outVec;\n",
    "p_0 = abs(val[1])^2;\n",
    "\n",
    "# the probability that Bob measures b = 1\n",
    "val = v1'*outVec;\n",
    "p_1 = abs(val[1])^2;\n",
    "\n",
    "# for printing, let's round the outcomes\n",
    "digits = 3;\n",
    "p_0 = round(p_0, digits);\n",
    "p_1 = round(p_1,digits);\n",
    "\n",
    "println(\"\\n\\n You entered U_1 =\")\n",
    "println(U_1)\n",
    "println(\"For this case the probability of Bob's measurement outcomes are:\")\n",
    "println(\"p_0 = $p_0\")\n",
    "println(\"p_1 = $p_1\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"bloch_sphere\"></a>\n",
    "<h2 style=\"color:#00A6D6;\">Bloch Sphere</h2>\n",
    "\n",
    "In class, we learned a different way to write down a qubit, namely in terms of the Bloch sphere. It is important to understand that this representation is fundamentally distinct from the 2 dimensional vectors we saw above. Instead, recall from the videos and the lecture notes that qubits are parameterized by angles $\\theta$ and $\\phi$ in the Bloch sphere representation. Be careful to note that we will use $\\theta/2$ here, since we will draw in a very different space in 3D than the one in the plots above.\n",
    "\n",
    "$$\\left| \\psi \\right\\rangle = cos \\frac{\\theta}{2} \\: \\left| 0 \\right\\rangle + e^{i \\cdot \\phi} sin \\frac{\\theta}{2} \\: \\left| 1 \\right\\rangle = \\begin{pmatrix} cos \\frac{\\theta}{2} \\\\ e^{i \\cdot \\phi} sin \\frac{\\theta}{2} \\end{pmatrix}$$\n",
    "\n",
    "Let us now see how the qubits Bloch sphere representation follows from $\\theta$ and $\\phi$. Explore where the state lies in terms of the angles in the animation below.\n",
    "\n",
    "<b> Click in the code bloch below and press shift+enter to run the animation. </b>\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Options{:ToggleButtons,Int64}(Signal{Int64}(15, nactions=0),\"view\",15,\"15\",Interact.OptionDict(Any[\"15\",\"60\",\"-30\"],Dict{Any,Any}(\"15\"=>15,\"-30\"=>-30,\"60\"=>60)),Any[],Any[])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Slider{Int64}(Signal{Int64}(90, nactions=0),\"θ\",90,0:30:180,true)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Slider{Int64}(Signal{Int64}(0, nactions=0),\"ϕ\",0,-180:30:180,true)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x00000000231C3588>)"
      ]
     },
     "execution_count": 64,
     "metadata": {
      "comm_id": "510850cd-306c-4928-a9b5-f1092f298e72",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# One can pick θ, ϕ using the sliders that appear when the code is run.\n",
    "\n",
    "f1 = figure(figsize=(8,8))        # make an empty figure\n",
    "\n",
    "@manipulate for view = [15,60,-30], θ in 0:30:180, ϕ in -180:30:180\n",
    "    b1 = Bloch()         # make an empty Bloch sphere\n",
    "    add_vector(b1,[θ,ϕ]) # add a vector, with \n",
    "    withfig(f1) do\n",
    "        render(b1,view) # render the bloch sphere (incl. the vector)\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is instructive to see what happens if we transform a vector on the Bloch sphere with a unitary. As an example let's consider the following state - you may want to adapt it to get more intuition!\n",
    "\n",
    "$$ \\lvert \\psi \\rangle = \\cos\\frac{\\pi}{8} \\cdot \\lvert 0 \\rangle + \\sin\\frac{\\pi}{8} \\cdot \\lvert 1 \\rangle $$\n",
    "\n",
    "$$= \\frac{ \\sqrt{2 + \\sqrt{2} }}{2} \\lvert 0 \\rangle + \\frac{ \\sqrt{2 - \\sqrt{2} }}{2}  \\vert 1 \\rangle $$\n",
    "\n",
    "We'll find the following images\n",
    "\n",
    "1. $ X \\cdot \\lvert \\psi \\rangle $\n",
    "2. $ Y \\cdot \\lvert \\psi \\rangle $\n",
    "3. $ Z \\cdot \\lvert \\psi \\rangle $\n",
    "4. $ H \\cdot \\lvert \\psi \\rangle $\n",
    "\n",
    "By running the code cell below you can see these states represented on the Bloch sphere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Options{:ToggleButtons,Int64}(Signal{Int64}(15, nactions=0),\"view\",15,\"15\",Interact.OptionDict(Any[\"15\",\"-30\",\"60\"],Dict{Any,Any}(\"15\"=>15,\"-30\"=>-30,\"60\"=>60)),Any[],Any[])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Options{:ToggleButtons,ASCIIString}(Signal{ASCIIString}(I, nactions=0),\"transform\",\"I\",\"I\",Interact.OptionDict(Any[\"I\",\"X\",\"Y\",\"Z\",\"H\"],Dict{Any,Any}(\"Y\"=>\"Y\",\"Z\"=>\"Z\",\"I\"=>\"I\",\"X\"=>\"X\",\"H\"=>\"H\")),Any[],Any[])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000025E5A7B8>)"
      ]
     },
     "execution_count": 65,
     "metadata": {
      "comm_id": "2f57f1d0-8744-4df4-b89f-d09f8884ab8c",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "α = 0.5*sqrt(2 + sqrt(2)) # the parameters α and β associated with the vector above - change at will.\n",
    "β = 0.5*sqrt(2 - sqrt(2)) # Note, changing α, β could help solve exercise 8.\n",
    "ket = [α; β];             # the associated vector\n",
    "\n",
    "# let us define the transforms\n",
    "pX = [0 1; 1 0]\n",
    "pY = [0 -im; im 0]\n",
    "pZ = [1 0; 0 -1]\n",
    "tH = [1 1; 1 -1]/sqrt(2)\n",
    "\n",
    "# we apply the I,X,Y,Z and H transvorm and find the corresponding Bloch vector using the function ket_to_bloch()\n",
    "v0 = ket_to_bloch(ket)      \n",
    "v1 = ket_to_bloch(pX*ket)    \n",
    "v2 = ket_to_bloch(pY*ket)    \n",
    "v3 = ket_to_bloch(pZ*ket)    \n",
    "v4 = ket_to_bloch(tH*ket)    \n",
    "\n",
    "# let us define a \"dictionary\": \"I\" belongs to v0, \"X\" belongs to v1, etc.\n",
    "vDict = Dict(   \"I\" => v0, \n",
    "                \"X\" => v1, \n",
    "                \"Y\" => v2, \n",
    "                \"Z\" => v3, \n",
    "                \"H\" => v4) \n",
    "\n",
    "# Now vDict[\"X\"] returns the vector v1.\n",
    "#     vDict[\"H\"] returns the vector v4.\n",
    "\n",
    "# let us create a new figure\n",
    "f9 = figure(figsize=(8,8)) \n",
    "\n",
    "# let us manipulate the view angle and the applied transform\n",
    "@manipulate for view in [15,-30,60], transform in [\"I\",\"X\",\"Y\",\"Z\",\"H\"]\n",
    "    \n",
    "    withfig(f9) do\n",
    "        b9 = Bloch()                 # make an empty Bloch sphere\n",
    "        add_vector(b9,v0)            # add the pre-transform Bloch vector\n",
    "        add_vector(b9,vDict[transform])    # add a transformed Bloch vector, \n",
    "                                           # note: vDict[] returns the vector associated with the transform \n",
    "        render(b9,view)      #  plot the Bloch Sphere\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 style=\"color:#00A6D6;\">edX Exercise 8 </h3>\n",
    "\n",
    "To become more familiar with the Bloch sphere, we ask you to find angles $\\theta$ and $\\phi$ (in radians) with \n",
    "\n",
    "$$ | \\psi \\rangle = cos \\frac{\\theta}{2} \\: | 0 \\rangle + e^{i \\cdot \\phi} sin \\frac{\\theta}{2} \\: | 1 \\rangle = \\begin{pmatrix} cos \\frac{\\theta}{2} \\\\ e^{i \\cdot \\phi} sin \\frac{\\theta}{2} \\end{pmatrix}$$\n",
    "\n",
    "for the following states\n",
    "\n",
    "1. $|\\psi \\rangle = |+\\rangle$\n",
    "2. $|\\psi \\rangle = \\frac{\\sqrt{3}}{2}|0\\rangle + \\frac{i}{2} \\cdot |1\\rangle $\n",
    "\n",
    "<b style=\"color:#00A6D6;\"> Example </b>\n",
    "\n",
    "To help you get started let us give one example. Let us find $\\theta$ and $\\phi$ associated with\n",
    "\n",
    "$$|\\psi \\rangle = |0\\rangle\\: :$$\n",
    "\n",
    "We are looking for $\\theta$, $\\phi$ such that\n",
    "\n",
    "$$|0\\rangle = cos \\frac{\\theta}{2} \\: | 0 \\rangle + e^{i \\cdot \\phi} sin \\frac{\\theta}{2} \\: | 1 \\rangle $$\n",
    "\n",
    "Thus $$\\alpha = cos \\frac{\\theta}{2} = 1 $$ and $$\\beta = e^{i \\cdot \\phi} sin \\frac{\\theta}{2} = 0 \\:.$$ We find as a solution $\\theta = 0$ ( $\\theta = k \\cdot 2\\pi$, $k$ integer ) with $\\phi$ irrelevant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style=\"color:#00A6D6;\"> Supplement to Exercise 7</h4>\n",
    "\n",
    "The code below can be used to vizualize the state on the Bloch sphere. Simply enter values for $\\theta$ and $\\phi$.\n",
    "\n",
    "To plot a state on the Bloch sphere we should determine the associated Bloch vector $v$ (a Cartesian vector):\n",
    "\n",
    "$$v = \\begin{pmatrix} v_x \\\\ v_y \\\\ v_z \\end{pmatrix} \\:.$$\n",
    " \n",
    "It turns out that $\\theta$ and $\\phi$ ---as introduced just now--- are the spherical coordinates coordinates associated with $v$. When it comes to the radial coordinate $r$, it turns out that $r=1$. This follows from $\\langle \\psi | \\psi \\rangle = 1$.\n",
    "\n",
    "Translating from spherical to Cartesian coordinates we recover\n",
    "\n",
    "$$ v = \\begin{pmatrix} \\sin\\theta \\cdot cos\\phi \\\\ \\sin\\theta \\cdot sin\\phi \\\\ \\cos\\theta \\end{pmatrix} $$ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Options{:ToggleButtons,Int64}(Signal{Int64}(15, nactions=0),\"view\",15,\"15\",Interact.OptionDict(Any[\"15\",\"-30\",\"60\"],Dict{Any,Any}(\"15\"=>15,\"-30\"=>-30,\"60\"=>60)),Any[],Any[])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000026143518>)"
      ]
     },
     "execution_count": 66,
     "metadata": {
      "comm_id": "dc1a63f8-1679-45a9-bb0e-91444df8242f",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = 60 # in degrees, change to your liking\n",
    "phi = 90    # in degrees\n",
    "\n",
    "# Side note: In the Julia language, sind(angle) takes as input an angle in degrees.\n",
    "#                                   sin(angle) takes as input an angle in radians.\n",
    "\n",
    "# Here we use degrees and thus sind, cosd\n",
    "\n",
    "bloch_vector = [sind(theta)*cosd(phi); sind(theta)*sind(phi); cosd(theta)]\n",
    "\n",
    "# the above can be altered to your liking, \n",
    "# define θ, ϕ either in terms of degrees or in terms of radians \n",
    "f8 = figure(figsize=(8,8))\n",
    "\n",
    "@manipulate for view in [15,-30,60]\n",
    "    withfig(f8) do\n",
    "        b8 = Bloch()                 # make an empty Bloch sphere\n",
    "        add_element(b8,bloch_vector) # add the vector to be plotted to the sphere\n",
    "        render(b8,view)              #  plot the Bloch Sphere\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc/4.0/88x31.png\" /></a><br /><span xmlns:dct=\"http://purl.org/dc/terms/\" property=\"dct:title\">Week 0 Exercises for QuCryptoX</span> by <a xmlns:cc=\"http://creativecommons.org/ns#\" href=\"http://qutech.nl/edu/\" property=\"cc:attributionName\" rel=\"cc:attributionURL\">QuTech Academy</a> is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc/4.0/\">Creative Commons Attribution-NonCommercial 4.0 International License</a>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Julia 0.5.0",
   "language": "julia",
   "name": "julia-0.5"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}