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Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations

1
International Center for Mathematical Modeling, Linnaeus University, 35195 Vaxjo, Sweden
2
Applied Mathematics Department, National Research University Higher School of Economics, 101000 Moscow, Russia
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(11), 829; https://doi.org/10.3390/e20110829
Received: 25 August 2018 / Revised: 5 October 2018 / Accepted: 22 October 2018 / Published: 29 October 2018
(This article belongs to the Special Issue Quantum Foundations: 90 Years of Uncertainty)
We introduce the general class of symmetric two-qubit states guaranteeing the perfect correlation or anticorrelation of Alice and Bob outcomes whenever some spin observable is measured at both sites. We prove that, for all states from this class, the maximal violation of the original Bell inequality is upper bounded by 3 2 and specify the two-qubit states where this quantum upper bound is attained. The case of two-qutrit states is more complicated. Here, for all two-qutrit states, we obtain the same upper bound 3 2 for violation of the original Bell inequality under Alice and Bob spin measurements, but we have not yet been able to show that this quantum upper bound is the least one. We discuss experimental consequences of our mathematical study. View Full-Text
Keywords: original Bell inequality; perfect correlation/anticorrelation; qudit states; quantum bound; measure of classicality original Bell inequality; perfect correlation/anticorrelation; qudit states; quantum bound; measure of classicality
MDPI and ACS Style

Khrennikov, A.Y.; Loubenets, E.R. Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations. Entropy 2018, 20, 829.

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