Bell inequalities for nonlocality depth

• URL: http://arxiv.org/abs/2205.04250v2
• Date: Thu, 9 Feb 2023 19:52:15 GMT
• Title: Bell inequalities for nonlocality depth
• Authors: Fabian Bernards and Otfried G\"uhne
• Abstract summary: When three or more particles are considered, quantum correlations can be stronger than correlations generated by so-called hybrid local hidden variable models. We provide an exhaustive classification of Bell inequalities to characterize various hybrid scenarios in four- and five-particle systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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