Bell inequalities for nonlocality depth

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.

12 pages, 3 figures, v2: final version

References in corpus (8)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Bounding the set of quantum correlations
• Bell nonlocality in networks
• Experimental violation of Svetlichny's inequality
• Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques
• Quantifying multipartite nonlocality via the size of the resource
• Exploring Bell inequalities for the device-independent certification of multipartite entanglement depth
• Finding optimal Bell inequalities using the cone-projection technique

Cited by in corpus (3)

• Tight upper bound for the maximal expectation value of the $N$-partite generalized Svetlichny operator
• Probing many-body Bell correlation depth with superconducting qubits
• Bell inequalities with overlapping measurements