The Extent of Multi-particle Quantum Non-locality

Abstract

It is well known that entangled quantum states can be nonlocal: the correlations between local measurements carried out on these states cannot always be reproduced by local hidden variable models. Svetlichny, followed by others, showed that multipartite quantum states are even more nonlocal than bipartite ones in the sense that nonlocal classical models with (super-luminal) communication between some of the parties cannot reproduce the quantum correlations. Here we study in detail the kinds of nonlocality present in quantum states. More precisely we enquire what kinds of classical communication patterns cannot reproduce quantum correlations. By studying the extremal points of the space of all multiparty probability distributions, in which all parties can make one of a pair of measurements each with two possible outcomes, we find a necessary condition for classical nonlocal models to reproduce the statistics of all quantum states. This condition extends and generalises work of Svetlichny and others in which it was shown that a particular class of classical nonlocal models, the ``separable'' models, cannot reproduce the statistics of all multiparticle quantum states. Our condition shows that the nonlocality present in some entangled multiparticle quantum states is much stronger than previously thought. We also study the sufficiency of our condition.

10 pages, 2 figures, journal version

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• Nonlocal setting and outcome information for violation of Bell's inequality
• Theory of genuine tripartite nonlocality of Gaussian states
• Anonymous Quantum Nonlocality
• Quantum communication complexity beyond Bell nonlocality
• Parts and Wholes. An Inquiry into Quantum and Classical Correlations
• Multipartite Nonlocality as a Resource and Quantum Correlations Having Indefinite Causal Order
• Optimal tests of genuine multipartite nonlocality
• Non-signaling Causal Hierarchy of General Multisource Networks
• Genuine multipartite nonlocality of permutationally invariant Gaussian states
• Structure of quantum and broadcasting nonlocal correlations
• Multistage games and Bell scenarios with communication
• Unbounded Bell violations for quantum genuine multipartite non-locality
• Mediated Digraphs and Quantum Nonlocality