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Quantum analog of the original Bell inequality for two-qudit states with perfect correlations/anticorrelations
Natl Res Univ, Russia.
Linnaeus University, Faculty of Technology, Department of Mathematics. (Int Ctr Math Modeling)ORCID iD: 0000-0002-9857-0938
2019 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, no 43, article id 435304Article in journal (Refereed) Published
Abstract [en]

For an even qudit dimension d >= 2, we introduce a class of two-qudit states exhibiting perfect correlations/anticorrelations and prove via the generalized Gell-Mann representation that, for each two-qudit state from this class, the maximal violation of the original Bell inequality is bounded from above by the value 3/2-the upper bound attained on some two-qubit states. We show that the two-qudit Greenberger-Horne-Zeilinger (GHZ) state with an arbitrary even d >= 2 exhibits perfect correlations/anticorrelations and belongs to the introduced two-qudit state class. These new results are important steps towards proving in general the 3/2 upper bound on quantum violation of the original Bell inequality. The latter would imply that similarly as the Tsirelson upper bound 2 root 2 specifies the quantum analog of the CHSH inequality for all bipartite quantum states, the upper bound 3/2 specifies the quantum analog of the original Bell inequality for all bipartite quantum states with perfect correlations/anticorrelations. Possible consequences for the experimental tests on violation of the original Bell inequality are briefly discussed.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2019. Vol. 52, no 43, article id 435304
Keywords [en]
the original Bell inequality, perfect correlations/anticorrelations, two-qudit quantum states, quantum violation, the 3/2 quantum upper bound
National Category
Physical Sciences Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-93142DOI: 10.1088/1751-8121/ab45c3ISI: 000518774900010Scopus ID: 2-s2.0-85073251018OAI: oai:DiVA.org:lnu-93142DiVA, id: diva2:1416969
Available from: 2020-03-26 Created: 2020-03-26 Last updated: 2020-12-14Bibliographically approved

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Khrennikov, Andrei

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  • apa
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  • de-DE
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