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arXiv:1812.10110 · Physical Review A

Güney-Hillery approach to Bell inequalities

Katarzyna Bolonek-Lasoń, Piotr Kosiński

Published May 24, 2019• 2 citations
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Abstract

We analyze certain aspects of the group-theoretical approach to Bell inequalities proposed by G\"uney and Hillery. The general procedure for constructing the relevant group orbits is described. Using Hall theorem we determine the form of Bell inequality in the single-orbit case. It is shown that in this case the Bell inequality is not violated for a maximally entangled state generating trivial subrepresentation if the representation under consideration is real.

DOI
10.1103/physreva.99.052122

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The recently proposed (Güney and Hillery in Phys Rev A 90:062121, 2014; Phys Rev A 91:052110, 2015) group theoretical approach to the problem of violating the Bell inequalities is applied to S4S_4S4​ group. The Bell inequalities based on the choice of three orbits in the representation space corresponding to standard representation of S4S_4S4​ are derived and their violation is described. The corresponding nonlocal games are analyzed.
Bell inequalities for S4S_4S4​ group: classical and quantum bounds for two orbits case
Within Guney-Hillery approach a number of examples of classical and quantum bounds on sum of probabilities resulting from two orbits of S4S_4S4​ is considered. It is shown that the violation of Bell's inequalities is rather rare and gentle.
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