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arXiv · 2205.04250

Bell inequalities for nonlocality depth

Fabian Bernards·Otfried Gühne
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Abstract

When three or more particles are considered, quantum correlations can be stronger than the correlations generated by so-called hybrid local hidden variable models, where some of the particles are considered as a single block inside which communication and signaling is allowed. We provide an exhaustive classification of Bell inequalities to characterize various hybrid scenarios in four- and five-particle systems. In quantum mechanics, these inequalities provide device-independent witnesses for the entanglement depth. In addition, we construct a family of inequalities to detect a non-locality depth of (n-1) in n-particle systems. Moreover, we present two generalizations of the original Svetlichny inequality, which was the first Bell inequality designed for hybrid models. Our results are based on the cone-projection technique, which can be used to completely characterize Bell inequalities under affine constraints; even for many parties, measurements, and outcomes.

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Fabian Bernards, Otfried Gühne. 2022-05-09. Bell inequalities for nonlocality depth. https://doi.org/10.1103/physreva.107.022412

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