Add arXiv reference

ComputeWitnessesAndRanges.nb

@@ -20,13 +20,13 @@ WindowFrame->Normal*)
 Notebook[{
 Cell[TextData[{
  "This notebook computes analytically the expressions of the witnesses of \
-triangle nonlocality obtained in arXiv:2203...... in \
+triangle nonlocality obtained in arXiv:2203.16543 in \
 \[OpenCurlyDoubleQuote]Bell inequality\[CloseCurlyDoubleQuote] form for ",
  StyleBox["symmetric",
   FontWeight->"Bold"],
  ", tripartite, binary-outcome distributions. Such model is proven not to \
 exist if an associated linear program, given in Appendix D of \
-arXiv:2203......, is infeasible. If the linear program is expressed as ",
+arXiv:2203.16543, is infeasible. If the linear program is expressed as ",
  Cell[BoxData[
   FormBox[
    RowBox[{
@@ -185,7 +185,7 @@ create the matrix ",
     FontWeight->"Bold"], TraditionalForm]],ExpressionUUID->
   "74b76e6e-8ee7-434c-9f4e-821f4ca52b6c"],
  " in the linear program. These are generated following the procedure of \
-Appendix D in arXiv:2203......."
+Appendix D in arXiv:2203.16543."
 }], "Text",
  CellChangeTimes->{{3.8507970899776773`*^9, 3.850797189799727*^9}, {
    3.851249644027876*^9, 3.8512496551166067`*^9}, 3.857354750771179*^9, 

README.md

@@ -1,7 +1,7 @@
-## Code to accompany *[Proofs of network quantum nonlocality aided by machine learning](https://www.arxiv.org/abs/2201.xxxxx)*
+## Code to accompany *[Proofs of network quantum nonlocality aided by machine learning](https://www.arxiv.org/abs/2203.16543)*
 #### Alejandro Pozas-Kerstjens, Nicolas Gisin, and Marc-Olivier Renou
 
-This is a repository containing the computational appendix of the article "*Proofs of network quantum nonlocality aided by machine learning*. Alejandro Pozas-Kerstjens, Nicolas Gisin, and Marc-Olivier Renou. [arXiv:2203.xxxxx](https://www.arxiv.org/abs/2203.xxxxx)." It provides the codes for setting up and solving the inflation problems that identify the distributions ![](https://latex.codecogs.com/svg.latex?q_u%5E%7Bt%3D-1%7D) as not admitting triangle-local models for the range ![](https://latex.codecogs.com/svg.latex?0.7504%5Cleq&space;u%5Cleq0.8101).
+This is a repository containing the computational appendix of the article "*Proofs of network quantum nonlocality aided by machine learning*. Alejandro Pozas-Kerstjens, Nicolas Gisin, and Marc-Olivier Renou. [arXiv:2203.16543](https://www.arxiv.org/abs/2203.16543)." It provides the codes for setting up and solving the inflation problems that identify the distributions ![](https://latex.codecogs.com/svg.latex?q_u%5E%7Bt%3D-1%7D) as not admitting triangle-local models for the range ![](https://latex.codecogs.com/svg.latex?0.7504%5Cleq&space;u%5Cleq0.8101).
 
 The code is written in Python and Mathematica.
 
@@ -30,13 +30,13 @@ Files:
 
 If you would like to cite this work, please use the following format:
 
-A. Pozas-Kerstjens, N. Gisin, and M.-O. Renou, _Proofs of network quantum nonlocality aided by machine learning_, arXiv:2203.xxxxx
+A. Pozas-Kerstjens, N. Gisin, and M.-O. Renou, _Proofs of network quantum nonlocality aided by machine learning_, arXiv:2203.16543
 
 ```
 @misc{pozaskerstjens2022triangle,
 author = {Pozas-Kerstjens, Alejandro and Gisin, Nicolas and Renou, Marc-Olivier},
 title = {{Proofs of network quantum nonlocality aided by machine learning}},
-eprint = {2203.xxxxx},
+eprint = {2203.16543},
 archivePrefix={arXiv}
 }
 ```

prove_full_range.py

@@ -1,6 +1,6 @@
 # Code for
 # Proofs of network quantum nonlocality aided by machine learning
-# arXiv:2203......
+# arXiv:2203.16543
 #
 # Authors: Alejandro Pozas-Kerstjens
 #
@@ -46,7 +46,7 @@ def evaluate_symbolic(LPA, LPb,
     :param b_values: Numerical values of the symbolic elements in the vector LPb
     :type b_values: numpy.array
     :param u: The value of the parameter u, inherited from the four-outcome
-              family of distributions in Eq. (2) in arXiv:2203.......
+              family of distributions in Eq. (2) in arXiv:2203.16543.
     :type u: float (1/sqrt(2) <= u <= 1)
     :param t: The value of the parameter t, which describes the orientation of
               the three excitations in the local model for the coarse-grained
@@ -108,7 +108,7 @@ def compute_new_u(y, A, b, u, t, direction):
     :param b: The vector of coefficients of the LP A.x >= b.
     :type b: numpy.array
     :param u: The value of the parameter u, inherited from the four-outcome
-              family of distributions in Eq. (2) in arXiv:2203.......
+              family of distributions in Eq. (2) in arXiv:2203.16543.
     :type u: float (1/sqrt(2) <= u <= 1)
     :param t: The value of the parameter t, which describes the orientation of
               the three excitations in the local model for the coarse-grained
@@ -165,7 +165,7 @@ def save_to_json(expression, expression_evaluation, u, expression_type):
                                   triangle-local model.
     :type expression_evaluation: float
     :param u: The value of the parameter u, inherited from the four-outcome
-              family of distributions in Eq. (2) in arXiv:2203.......
+              family of distributions in Eq. (2) in arXiv:2203.16543.
     :type u: float (1/sqrt(2) <= u <= 1)
     :param filename: The name of the file to be saved.
     :type filename: str

test_one_point.py

@@ -1,6 +1,6 @@
 # Code for
 # Proofs of network quantum nonlocality aided by machine learning
-# arXiv:2203......
+# arXiv:2203.16543
 #
 # Authors: Alejandro Pozas-Kerstjens
 #

utils.py

@@ -1,6 +1,6 @@
 # Code for
 # Proofs of network quantum nonlocality aided by machine learning
-# arXiv:2203......
+# arXiv:2203.16543
 #
 # Authors: Alejandro Pozas-Kerstjens
 #
@@ -51,7 +51,7 @@ def create_basic_inflation_LP(self):
         positive and summing to 1, and the symmetries derived from the
         invariance under permutation of copies of the sources. This is, it
         implements the constraints described in Eqs. (C1), (C2) and (C3) in
-        arXiv:2203......
+        arXiv:2203.16543
         '''
         # Positivity constraints
         np.fill_diagonal(self.LPA, 1)
@@ -108,7 +108,7 @@ def add_hierarchy_constraints(self, distribution, create_symbolicb=False):
         relate the probability distribution in the inflation to the original,
         that are at most polynomials of the same order of the inflation. This
         is, it adds the "hierarchy constraints" described by Eq. (C4) in
-        arXiv:2203....... Optionally it generates an abstract values
+        arXiv:2203.16543. Optionally it generates an abstract values
         vector, which is useful for deriving nonlocality witnesses at a later
         stage.
 
@@ -146,7 +146,7 @@ def add_higher_order_constraints(self, distribution):
         relate the probability distribution in the inflation to the original,
         that involve polynomials of order higher than the inflation level.
         This is, it adds the "higher-order constraints" described in Eq. (C5) in
-        arXiv:2201.......
+        arXiv:2203.16543.
 
         :param distribution: Probability distribution under test.
         :type distribution: numpy.array
@@ -179,7 +179,7 @@ def add_lpi_constraints(self, distribution, create_symbolicA=False):
         relate the probability distribution in the inflation to the original,
         that are at most polynomials of the same order of the inflation. This
         is, it adds the "hierarchy constraints" described in Eq. (C6) in
-        arXiv:2201....... Optionally it generates an abstract coefficient
+        arXiv:2203.16543. Optionally it generates an abstract coefficient
         matrix, which is useful for deriving nonlocality witnesses at a later
         stage.
 
@@ -261,10 +261,10 @@ def _to_indices(self, position):
 def RGB4_two_outcomes(u, FAB, FAC, FBC, FABC, t, dtype='float64'):
     '''
     The family of binary-outcome probability distributions q_u^{t}(i,j,k)
-    described in Eq. (3) of arXiv:2203.......
+    described in Eq. (3) of arXiv:2203.16543.
 
     :param u: The value of the parameter u, inherited from the four-outcome
-              family of distributions in Eq. (2) in arXiv:2203.......
+              family of distributions in Eq. (2) in arXiv:2203.16543.
     :type u: float (1/sqrt(2) <= u <= 1)
     :param FAB: The value of the free parameter F_AB.
     :type FAB: float
@@ -302,10 +302,10 @@ def RGB4_two_outcomes(u, FAB, FAC, FBC, FABC, t, dtype='float64'):
 
 def generate_polytope(u, FAB, FAC, FBC, FABC):
     '''Provides the inequalities describing the polytope of valid probability
-    distributions in Eqs. (A1) of arXiv:2203......, for the given value of u.
+    distributions in Eqs. (A1) of arXiv:2203.16543, for the given value of u.
 
     :param u: The value of the parameter u, inherited from the four-outcome
-              family of distributions in Eq. (2) in arXiv:2203.......
+              family of distributions in Eq. (2) in arXiv:2203.16543.
     :type u: float (1/sqrt(2) <= u <= 1)
     :param FAB: Symbol representing the free parameter F_AB.
     :type FAB: sympy.Symbol
@@ -517,7 +517,7 @@ def ineq_intersects_faces(ineq, u, t):
     :param ineq: The certificate of infeasibility obtained from Frakas' lemma
     :type ineq: sympy.core.expr.Expr
     :param u: The value of the parameter u, inherited from the four-outcome
-              family of distributions in Eq. (2) in arXiv:2203.......
+              family of distributions in Eq. (2) in arXiv:2203.16543.
     :type u: float (1/sqrt(2) <= u <= 1)
     :param t: The value of the parameter t, which describes the orientation of
               the three excitations in the local model for the coarse-grained

vertex_functions.py

@@ -1,6 +1,6 @@
 # Code for
 # Proofs of network quantum nonlocality aided by machine learning
-# arXiv:2203......
+# arXiv:2203.16543
 #
 # Authors: Alejandro Pozas-Kerstjens
 #
@@ -13,7 +13,7 @@ def get_polytope_vertices(u):
     '''For a value of u, obtain the vertices of the feasible poltope.
 
     :param u: The value of the parameter u, inherited from the four-outcome
-              family of distributions in Eq. (2) in arXiv:2203.......
+              family of distributions in Eq. (2) in arXiv:2203.16543.
     :type u: float (1/sqrt(2) <= u <= 1)
 
     :returns funs: list of vertex functions.