Bell inequalities from group actions: Three parties and non-Abelian groups

TL;DR

This paper extends a method for deriving Bell inequalities using group actions to three-party scenarios and non-Abelian groups, providing new tools to analyze quantum nonlocality.

Contribution

It introduces a generalized approach to generate Bell inequalities from group actions involving three parties and non-Abelian groups, expanding previous two-party, Abelian group methods.

Findings

Derived new Bell inequalities for three-party systems

Extended the group action method to non-Abelian groups

Discussed implications for nonlocal games

Abstract

In a previous publication, we showed how group actions can be used to generate Bell inequalities. The group action yields a set of measurement probabilities whose sum is the basic element in the inequality. The sum has an upper bound if the probabilities are a result of a local, realistic theory, but this bound can be violated if the probabilities come from quantum mechanics. In our first paper, we considered the case of only two parties making the measurements and single-generator groups. Here we show that the method can be extended to three parties, and it can also be extended to non-Abelian groups. We discuss the resulting inequalities in terms of nonlocal games.