Abstract
We explore a connection between monogamy of non-locality and a weak macroscopic locality condition: the locality of the average behaviour. These are revealed by our analysis as being two sides of the same coin. Moreover, we exhibit a structural reason for both in the case of Bell-type multipartite scenarios, shedding light on but also generalising the results in the literature [16, 14]. More specifically, we show that, provided the number of particles in each site is large enough compared to the number of allowed measurement settings, and whatever the microscopic state of the system, the macroscopic average behaviour is local realistic, or equivalently, general multipartite monogamy relations hold. This result relies on a classical mathematical theorem by Vorob'ev [18] about extending compatible families of probability distributions defined on the faces of a simplicial complex - in the language of the sheaf-theoretic framework of Abramsky & Brandenburger [2], such families correspond to no-signalling empirical models, and the existence of an extension corresponds to locality or noncontextuality. Since Vorob'ev's theorem depends solely on the structure of the simplicial complex, which encodes the compatibility of the measurements, and not on the specific probability distributions (i.e. The empirical models), our result about monogamy relations and locality of macroscopic averages holds not just for quantum theory, but for any empirical model satisfying the no-signalling condition. In this extended abstract, we illustrate our approach by working out a couple of examples, which convey the intuition behind our analysis while keeping the discussion at an elementary level.
Original language | English |
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Title of host publication | Proceedings of the 11th Workshop on Quantum Physics and Logic, QPL |
Subtitle of host publication | 2014, Kyoto, Japan, 4-6th June 2014. |
Editors | B. Coecke, I. Hasuo, P. Panangaden |
Pages | 36-55 |
Number of pages | 20 |
Volume | 172 |
DOIs | |
Publication status | Published - 2014 |
Event | 11th Workshop on Quantum Physics and Logic - Grad. School of Science Seminar House at the Kyoto University Campus, Kyoto, Japan Duration: 4 Jun 2014 → 6 Jun 2014 Conference number: 11 http://group-mmm.org/qpl2014/ |
Publication series
Name | Electronic Proceedings in Theoretical Computer Science, EPTCS |
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Publisher | Open Publishing Association |
Volume | 172 |
ISSN (Print) | 2075-2180 |
Conference
Conference | 11th Workshop on Quantum Physics and Logic |
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Abbreviated title | QPL 2014 |
Country/Territory | Japan |
City | Kyoto |
Period | 4/06/14 → 6/06/14 |
Internet address |
Keywords / Materials (for Non-textual outputs)
- Bell inequalities
- Macroscopic averages
- Monogamy of non-locality
- No-signalling models
- Simplicial complexes
- Vorob'ev's theorem