### 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 to 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. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.

Original language | English |
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Article number | 424029 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 47 |

Issue number | 42 |

DOIs | |

Publication status | Published - Oct 24 2014 |

### Keywords

- closed sets of correlations
- quantum distillation
- quantum nonlocality

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*47*(42), [424029]. https://doi.org/10.1088/1751-8113/47/42/424029