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 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

10 pages and 8 figures. Updated to match the published version

References in corpus (1)

• Beyond Bell's Theorem: Correlation Scenarios

Cited by in corpus (6)

• Post-quantum nonlocality in the minimal triangle scenario
• Closing the detection loophole in the triangle network with high-dimensional photonic states
• Discovering Local Hidden-Variable Models for Arbitrary Multipartite Entangled States and Arbitrary Measurements
• Local models and Bell inequalities for the minimal triangle network
• Symmetric observations without symmetric causal explanations
• Experimental genuine quantum nonlocality in the triangle network