### 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 |
---|---|

Article number | 424029 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 47 |

Issue number | 42 |

DOIs | |

Publication status | Published - Oct 24 2014 |

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### Keywords

- closed sets of correlations
- quantum distillation
- quantum nonlocality

### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

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

**Closed sets of correlations : Answers from the zoo.** / Lang, Ben; Vértesi, T.; Navascués, Miguel.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 47, no. 42, 424029. https://doi.org/10.1088/1751-8113/47/42/424029

}

TY - JOUR

T1 - Closed sets of correlations

T2 - Answers from the zoo

AU - Lang, Ben

AU - Vértesi, T.

AU - Navascués, Miguel

PY - 2014/10/24

Y1 - 2014/10/24

N2 - 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'.

AB - 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'.

KW - closed sets of correlations

KW - quantum distillation

KW - quantum nonlocality

UR - http://www.scopus.com/inward/record.url?scp=84907822090&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907822090&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/47/42/424029

DO - 10.1088/1751-8113/47/42/424029

M3 - Article

AN - SCOPUS:84907822090

VL - 47

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 42

M1 - 424029

ER -