Closed sets of correlations: answers from the zoo

Lang, B. and Vértesi, Tamás and Navascués, M. (2014) Closed sets of correlations: answers from the zoo. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 47 (42). ISSN 1751-8113

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Abstract

We investigate the conditions under which a set of multipartite nonlo- cal correlations can describe the distributions achievable by distant par- ties 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 conjec- tures 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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