Quantifying Bell nonlocality of a pure two-qudit state via its entanglement

For the maximal violation of all Bell inequalities by an arbitrary pure two-qudit state of any dimension, we derive a new lower bound expressed via the concurrence of this pure state. This new lower bound and the upper bound on the maximal Bell violation, found in Loubenets and Namkung (2022 J. Phys...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2024-02, Vol.57 (5), p.55302
Main Authors: Loubenets, Elena R, Kuznetsov, Sergey, Hanotel, Louis
Format: Article
Language:English
Subjects:
Bell nonlocality
concurrence
nonlocality measure
quantum entanglement
two-qudit states
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Summary:For the maximal violation of all Bell inequalities by an arbitrary pure two-qudit state of any dimension, we derive a new lower bound expressed via the concurrence of this pure state. This new lower bound and the upper bound on the maximal Bell violation, found in Loubenets and Namkung (2022 J. Phys. A: Math. Theor. 55 285301) and also expressed via the concurrence, analytically quantify Bell nonlocality of a pure two-qudit state via its entanglement, in particular, prove explicitly that entanglement of a pure two-qudit state is necessary and sufficient for its Bell nonlocality. By re-visiting the pure two-qubit case, we also find and rigorously prove the new results on correlation properties of an arbitrary pure two-qubit state.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ad1b74