Generalized Clauser-Horne-Shimony-Holt inequalities maximally violated by higher dimensional systems

TL;DR

This paper introduces new Bell inequalities that extend CHSH and demonstrates that their maximum quantum violations require higher-dimensional systems beyond qubits.

Contribution

The paper proposes generalized Bell inequalities and proves that their maximal quantum violations are achieved only with higher-dimensional quantum systems.

Findings

New families of Bell inequalities generalizing CHSH

Maximum quantum violation requires higher-dimensional systems

Quantum violations exceed qubit-based limits

Abstract

Imagine two parties, Alice and Bob who share an entangled quantum state. A well-established result that if Alice performs two-outcome measurement on the portion of the state in her possession and Bob does likewise, they are able to produce correlations that cannot be reproduced by any classical theory. The allowed classical correlations can be expressed quantitatively by the Bell inequalities. Here we propose new families of Bell inequalities, as a generalization of the Clauser-Horne-Shimony-Holt (CHSH) inequality and show that the maximum violation of these Bell inequalities allowed by quantum theory can not be attained by a bipartite quantum system having support on a qubit at each site.