Code to accompany Proofs of network quantum nonlocality in continuous families of distributions

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 in continuous families of distributions. Alejandro Pozas-Kerstjens, Nicolas Gisin, and Marc-Olivier Renou. Phys. Rev. Lett. 130, 090201 (2023), arXiv:2203.16543." It provides the codes for setting up and solving the inflation problems that identify the distributions as not admitting triangle-local models for the range .

The code is written in Python and Mathematica.

Python libraries required:

• numpy for math operations
• sympy for symbolic operations
• scipy for root finding
• wolframclient for interaction with Wolfram Mathematica
• mosek for solving the linear programming problems
• (optional) gurobipy for solving the linear programming problems
• argparse, itertools, json, math, os

Files:

• certificatesExpressionsAndValidities: Table containing the expressions of the witnesses in (symmetric) correlator form, along with the range in which they witness that the distributions do not admit a triangle local model.

• ComputeWitnessesAndRanges: Takes the certificates of infeasibility of the inflation linear programs created in prove_full_range and converts them into inequalities valid for arbitrary binary-outcome distributions. It also computes explicitly the range of validity for when evaluated on the distributions .

• prove_full_range: For a specified initial value of , iteratively check whether admits a triangle-local model, and if not compute until which value of the corresponding certificate witnesses as not admitting a triangle-local model. Usage: prove_full_range.py -u u_init (default=0.8101) -s solver (default mosek) -d direction_of_uprime (default decrease) -save save_expressions (default False).

• test_one_point: For a specified value of , check if the distribution evaluated at the most relevant vertex of the polytope of allowed parameter values admits a triangle-local model. Usage: prove_full_range.py -u u_init (required) -s solver (default mosek) -save save_the_certificate (default False).

• utils: additional functions.

• vertex_functions: definition of functions that provide the coordinates of all the points that are vertices of the polytope at some value of .

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 in continuous families of distributions, Phys. Rev. Lett. 130, 090201 (2023), arXiv:2203.16543

@article{pozaskerstjens2022triangle,
  title = {Proofs of Network Quantum Nonlocality in Continuous Families of Distributions},
  author = {Pozas-Kerstjens, Alejandro and Gisin, Nicolas and Renou, Marc-Olivier},
  journal = {Phys. Rev. Lett.},
  volume = {130},
  issue = {9},
  pages = {090201},
  numpages = {6},
  year = {2023},
  month = {Feb},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.130.090201},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.130.090201},
  archivePrefix = {arXiv},
  eprint = {2203.16543}
}