Tight Correlation-Function Bell Inequality for Multipartite $d$-Dimensional System

TL;DR

This paper extends the CHSH Bell inequality to multipartite d-dimensional systems, providing a simple, tight, and potentially optimal form that unifies and generalizes previous inequalities, including the CGLMP inequality.

Contribution

The authors introduce a generalized correlation-function Bell inequality for multipartite d-dimensional systems that is simple, tight, and encompasses previous inequalities like CGLMP.

Findings

The new inequalities are tight for small systems.

They are likely tight for higher-dimensional systems.

The inequalities unify and generalize existing Bell inequalities.

Abstract

We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to multipartite d-dimensional systems. All the Bell inequalities based on this generalization take the same simple form as the CHSH inequality. For small systems, numerical results show that the new inequalities are tight and we believe this is also valid for higher dimensional systems. Moreover, the new inequalities are relevant to the previous ones and for bipartite system, our inequality is equivalent to the Collins-Gisin-Linden-Masser-Popescu (CGLMP) inequality.