Tight Bell inequalities from polytope slices

TL;DR

This paper derives new tight Bell inequalities for various bipartite scenarios, providing comprehensive facet lists and analyzing their quantum violations, noise resistance, and detection efficiency, with potential applications in quantum communication.

Contribution

It presents the complete set of facets for several bipartite Bell polytopes and analyzes their quantum violations and robustness, advancing the understanding of Bell inequalities in complex scenarios.

Findings

Complete facet sets for multiple bipartite scenarios.

Identification of scenarios outperforming CHSH in noise resistance.

Quantitative analysis of quantum violations and detection efficiencies.

Abstract

We derive new tight bipartite Bell inequalities for various scenarios. A bipartite Bell scenario $(X,Y,A,B)$ is defined by the numbers of settings and outcomes per party, $X$, $A$ and $Y$, $B$ for Alice and Bob, respectively. We derive the complete set of facets of the local polytopes of $(6,3,2,2)$, $(3,3,3,2)$, $(3,2,3,3)$, and $(2,2,3,5)$. We provide extensive lists of facets for $(2,2,4,4)$, $(3,3,4,2)$ and $(4,3,3,2)$. For each inequality we compute the maximum quantum violation, the resistance to noise, and the minimal symmetric detection efficiency required to close the detection loophole, for qubits, qutrits and ququarts. Based on these results, we identify scenarios which perform better in terms of visibility, resistance to noise, or both, when compared to CHSH. Such scenarios could find important applications in quantum communication.