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arXiv · 1905.11317

Quantum analog of the original Bell inequality for two-qudit states with perfect correlations/anticorrelations

Elena R. Loubenets·Andrei Y. Khrennikov
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Abstract

For an even qudit dimension $d\geq 2,$ 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 $d\geq 2$ exhibits perfect correlations/anticorrelations and belongs to the introduced two-qudit state class. These new results are important steps towards proving in general the $\frac{3}{2}$ upper bound on quantum violation of the original Bell inequality. The latter would imply that similarly as the Tsirelson upper bound $2\sqrt{2}$ specifies the quantum analog of the CHSH inequality for all bipartite quantum states, the upper bound $\frac{3}{2}$ 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.

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Elena R. Loubenets, Andrei Y. Khrennikov. 2019-05-27. Quantum analog of the original Bell inequality for two-qudit states with perfect correlations/anticorrelations. https://doi.org/10.1088/1751-8121%2Fab45c3

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