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arXiv · 1402.2850

Closed sets of correlations: answers from the zoo

Ben Lang·Tamas Vertesi·Miguel Navascues
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Abstract

We investigate the conditions under which a set of multipartite nonlocal correlations can describe the distributions achievable by distant parties conducting experiments in a consistent universe. Several questions are posed, such as: are all such sets "nested", i.e., contained into one another? Are they discrete or do they form a continuum? How many of them are supraquantum? Are there non-trivial polytopes among them? We answer some of these questions or relate them with established conjectures in complexity theory by introducing a "zoo" of physically consistent sets which can be characterized efficiently via either linear or semidefinite programming. As a bonus, we use the zoo to derive, for the first time, concrete impossibility results in nonlocality distillation.

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Ben Lang, Tamas Vertesi, Miguel Navascues. 2014-02-12. Closed sets of correlations: answers from the zoo. https://doi.org/10.1088/1751-8113/47/42/424029

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