Numerical Determination of Local Models in Networks

Abstract

Taking advantage of the fact that the cardinalities of hidden variables in network scenarios can be taken 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 applied to get numerical estimates to two interesting problems in the context of network non-locality: i) for which critical visibility the Greenberger-Horne-Zeilinger (GHZ) distribution ceases to be local in the triangle scenario with no inputs; ii) what is the boundary of the local set in a given 2-dimensional slice of the probability space for the bilocal network with binary inputs and outputs. For the first problem: a critical visibility of v ≈ 1/3 was found; behaviours with v ≤ 1/3 were proven to be trilocal; and numerical evidence that behaviours with v > 1/3 are not trilocal was found. For the second problem: a closed set that approximates the bilocal set was found; behaviours inside this set were proven to be bilocal; and numerical evidence that behaviours outside this set are not bilocal was found.