Numerically assisted determination of local models in network scenarios
Abstract
Taking advantage of the fact that the cardinalities of hidden variables in network scenarios can be assumed to be finite without loss of generality, a numerical tool for finding explicit local models that reproduce a given statistical behaviour was developed. The numerical procedure was then validated using families of statistical behaviours for which the networklocal boundary is known, in the bilocal scenario. Furthermore, the critical visibility for 3 notable distributions mixed with a uniform random noise is investigated in the triangle network without inputs. We provide conjectures for the critical visibilities of the GreenbergerHorneZeilinger (GHZ) and W distributions (which are roots of 4th degree polynomials), as well as a lower bound estimate of the critical visibility of the Elegant Joint Measurement distribution. The developed codes and documentation are publicly available at github.com/mariofilho281/localmodels
 Publication:

arXiv eprints
 Pub Date:
 March 2023
 DOI:
 10.48550/arXiv.2303.09954
 arXiv:
 arXiv:2303.09954
 Bibcode:
 2023arXiv230309954M
 Keywords:

 Quantum Physics
 EPrint:
 10 pages and 7 figures