Closed sets of correlations: answers from the zoo

Lang, Ben; Vértesi, Tamás; Navascués, Miguel

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.

• Journal Article Type: Article
• Acceptance Date: Apr 25, 2014
• Online Publication Date: Oct 8, 2014
• Publication Date: Oct 8, 2014
• Deposit Date: May 22, 2024
• Publicly Available Date: May 24, 2024
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 47
• Issue: 42
• Article Number: 424029
• DOI: https://doi.org/10.1088/1751-8113/47/42/424029
• Public URL: https://nottingham-repository.worktribe.com/output/34871536
• Publisher URL: https://iopscience.iop.org/article/10.1088/1751-8113/47/42/424029