Numerically assisted determination of local models in network scenarios

• URL: http://arxiv.org/abs/2303.09954v3
• Date: Sat, 4 Nov 2023 15:50:40 GMT
• Title: Numerically assisted determination of local models in network scenarios
• Authors: Jos\'e M\'ario da Silva and Fernando Parisio
• Abstract summary: We develop a numerical tool for finding explicit local models that reproduce a given statistical behaviour. We provide conjectures for the critical visibilities of the Greenberger-Horne-Zeilinger (GHZ) and W distributions. The developed codes and documentation are publicly available at281.com/mariofilho/localmodels.
• Score: 55.2480439325792
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 network-local 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 Greenberger-Horne-Zeilinger (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

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