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Violations of Bell inequalities from random pure states

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Atkin, Max R. [UCL] Zohren, Stefan [University of Oxford]

We consider the expected violations of Bell inequalities from random pure states. More precisely, we focus on a slightly generalized version of the Collins-Gisin-Linden-Massar-Popescu inequality, which concerns Bell experiments of two parties, two measurement options, and N outcomes, and analyze their expected quantum violations from random pure states for varying N, assuming the conjectured optimal measurement operators. It is seen that for small N the Bell inequality is not violated on average, while for larger N it is. Both ensembles of unstructured as well as structured random pure states are considered. Using techniques from random matrix theory this is obtained analytically for small and large N and numerically for intermediate N. The results show a beautiful interplay of different aspects of random matrix theory, ranging from the Marchenko-Pastur distribution and fixed-trace ensembles to the O(n) model.

Document type Article de périodique (Journal article) – Article de recherche
Publication date 2015
Language Anglais
Journal information "Physical Review A" - Vol. 92, no.1, p. 012331 (2015)
Publisher American Physical Society (APS)
issn 1050-2947
e-issn 1094-1622
Publication status Soumis
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
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Bibliographic reference Atkin, Max R. ; Zohren, Stefan. Violations of Bell inequalities from random pure states. In: Physical Review A, Vol. 92, no.1, p. 012331 (2015)
Permanent URL http://hdl.handle.net/2078.1/199267