Non-locality distillation and post-quantum theories with trivial communication complexity

Abstract

We first present a protocol for deterministically distilling non-locality, building upon a recent result of Forster et al. [Phys. Rev. Lett. 102, 120401 (2009)]. Our protocol, which is optimal for two-copy distillation, works efficiently for a specific class of post-quantum non-local boxes, which we term correlated non-local boxes. In the asymptotic limit, all correlated non-local boxes are distilled to the maximally non-local box of Popescu and Rohrlich. Then, taking advantage of a result of Brassard \textit{et al.} [Phys. Rev. Lett. 96, 250401 (2006)] we show that all correlated non-local boxes make communication complexity trivial, and therefore appear very unlikely to exist in nature. Astonishingly, some of these non-local boxes are arbitrarily close to the set of classical correlations. This result therefore gives new insight to the problem of why quantum non-locality is limited.

4 pages, 4 figures. To Appear in PRL

References in corpus (9)

• Non-local correlations as an information theoretic resource
• Bounding the set of quantum correlations
• A limit on nonlocality in any world in which communication complexity is not trivial
• General properties of Nonsignaling Theories
• No quantum advantage for nonlocal computation
• Detection loophole in asymmetric Bell experiments
• Minimum detection efficiency for a loophole-free atom-photon Bell experiment
• Distilling Non-Locality
• Emergence of Quantum Correlations from Non-Locality Swapping

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