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

• URL: http://arxiv.org/abs/2303.16794v2
• Date: Wed, 16 Aug 2023 16:04:38 GMT
• Title: Quantifying Bell nonlocality of a pure two-qudit state via its entanglement
• Authors: Elena R. Loubenets, Sergey Kuznetsov and Louis Hanotel
• Abstract summary: We find that entanglement of a pure two-qudit state is necessary and sufficient for its Bell nonlocality. We rigorously prove the new results on the correlation properties of an arbitrary pure two-qubit state.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 [J. Phys. A: Math. Theor. 55, 285301 (2022)] 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 the correlation properties of an arbitrary pure two-qubit state.

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