Axiomatic approach for the functional bound of generic Bell's inequality

TL;DR

This paper introduces an axiomatic formalism to determine the maximal bounds of generalized Bell inequalities, simplifying the optimization process and unifying various known Bell functions within a single framework.

Contribution

The authors develop a formalism that derives bounds for generalized Bell inequalities and applies it to generate and analyze various known Bell functions.

Findings

The formalism reduces the complexity of finding bounds to counting problems.

It can generate many known Bell functions such as Mermin, Ardehali, Svetlichny.

The approach provides a systematic way to analyze Bell inequalities.

Abstract

We propose a formalism to derive the maximal bound of generalized Bell type inequalities and shows that the formalism can be applied to various form of Bell functions. The generic Bell function is defined to generate the combinations of all the possible correlations whose local realistic bound can be obtained from the series of the constraint equations. The application of the constraints converts the optimization problem into the counting problems whose complexity is dramatically reduced. It is also shown that generic Bell function can be used to generate many other known Bell type functions such as Mermin, Ardehali, Svetlichny functions for multipartite two-dimensional class.