Necessary and sufficient conditions for multipartite Bell violations with only one trusted device

Abstract

We study multipartite Bell nonlocality in a framework native of multipartite Einstein-Podolsky-Rosen (EPR) steering scenarios with a single trusted measurement device. We derive a closed-form necessary and sufficient criterion for systems composed of a qubit and N-1 untrusted black-box measurement devices to violate -- under general dichotomic measurements on the qubit -- a generic Bell inequality from a broad family of linear inequalities with arbitrarily many outputs for the N-1 untrusted devices and inputs for all N parties. The optimal quantum measurements for maximal violation are also obtained. For two users, and two inputs and two outputs per user, our criterion becomes necessary and sufficient for Bell nonlocality. Furthermore, in that setting, its form generalizes recently obtained steering inequalities, which allows us to provide useful feedback from nonlocality to the detection of steering. Our findings constitute a practical tool for the study of the interplay between EPR steering and Bell nonlocality, with potential applications in multipartite information processing.

v2: main results explicitly generalized to the multipartite scenario. Main paper: 5 pages, 1 figure; 9 pages in total

References in corpus (8)

• Device-independent security of quantum cryptography against collective attacks
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Significant-loophole-free test of Bell's theorem with entangled photons
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• All bipartite entangled states display some hidden nonlocality
• Analog of the Clauser-Horne-Shimony-Holt inequality for steering
• All quantum states useful for teleportation are nonlocal resources

Cited by in corpus (8)

• Quantum steering: a review with focus on semidefinite programming
• Quantum steerability: characterization, quantification, superactivation and unbounded amplification
• Anisotropic invariance and the distribution of quantum correlations
• Quantum steering beyond instrumental causal networks
• The intrinsic relations of quantum resources in multiparticle systems
• Experimental Verification of Anisotropic Invariance for Three-Qubit States
• Exposure of subtle multipartite quantum nonlocality
• Violation of space-time Bell-CHSH inequality beyond Tsirelson bound via post selection and quantum cryptography