CHSH type Bell inequalities involving a party with two or three local binary settings

TL;DR

This paper presents an algorithm to generate Bell inequalities involving multiple measurement settings and observers, enabling the construction of new inequalities for complex quantum systems.

Contribution

The authors introduce a simple algorithm to generate CHSH-type Bell inequalities with additional measurement settings and observers, extending previous methods.

Findings

Algorithm successfully generates inequalities with two or three settings.

New symmetric inequalities for four observers with three settings each.

Analysis shows potential for exploring quantum nonlocality in complex systems.

Abstract

We construct a simple algorithm to generate any CHSH type Bell inequality involving a party with two local binary measurements from two CHSH type inequalities without this party. The algorithm readily generalizes to situations, where the additional observer uses three measurement settings. There, each inequality involving the additional party is constructed from three inequalities with this party excluded. With this generalization at hand, we construct and analyze new symmetric inequalities for four observers and three experimental settings per observer.