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Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations
Linnaeus University, Faculty of Technology, Department of Mathematics. National Research University Higher School of Economics, Russia.ORCID iD: 0000-0002-9857-0938
National Research University Higher School of Economics, Russia.
2018 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 20, no 11, article id 829Article in journal (Refereed) Published
Abstract [en]

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 32" role="presentation">32 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 32" role="presentation">32 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.

Place, publisher, year, edition, pages
MDPI, 2018. Vol. 20, no 11, article id 829
Keywords [en]
original Bell inequality; perfect correlation/anticorrelation; qudit states; quantum bound; measure of classicality
National Category
Computational Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-79077DOI: 10.3390/e20110829ISI: 000451308800021Scopus ID: 2-s2.0-85057064996OAI: oai:DiVA.org:lnu-79077DiVA, id: diva2:1268224
Available from: 2018-12-05 Created: 2018-12-05 Last updated: 2019-08-29Bibliographically approved

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Khrennikov, Andrei

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