Bell inequalities from variable elimination methods

TL;DR

This paper introduces an alternative algebraic and variable elimination approach to derive tight Bell inequalities, overcoming computational challenges and explaining the finite families of inequalities in complex measurement scenarios.

Contribution

It presents a novel method combining measure extension results and variable elimination techniques to find Bell inequalities more efficiently.

Findings

Method overcomes computational difficulties in certain cases.

Explains the finite number of Bell inequality families in complex scenarios.

Provides a new perspective on deriving Bell inequalities.

Abstract

Tight Bell inequalities are facets of Pitowsky's correlation polytope and are usually obtained from its extreme points by solving the hull problem. Here we present an alternative method based on a combination of algebraic results on extensions of measures and variable elimination methods, e.g., the Fourier-Motzkin method. Our method is shown to overcome some of the computational difficulties associated with the hull problem in some non-trivial cases. Moreover, it provides an explanation for the arising of only a finite number of families of Bell inequalities in measurement scenarios where one experimenter can choose between an arbitrary number of different measurements.