Closed sets of correlations: Answers from the zoo

Ben Lang, T. Vértesi, Miguel Navascués

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 languageEnglish
Article number424029
JournalJournal of Physics A: Mathematical and Theoretical
Volume47
Issue number42
DOIs
Publication statusPublished - Oct 24 2014

Fingerprint

polytopes
linear programming
distillation
programming
Closed set
bells
Distillation
Physics
theorems
universe
Concretes
continuums
conduction
physics
Nonlocality
Complexity Theory
Experiments
Semidefinite Programming
Polytopes
Linear programming

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

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

In: Journal of Physics A: Mathematical and Theoretical, Vol. 47, No. 42, 424029, 24.10.2014.

Research output: Contribution to journalArticle

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