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

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.

arXiv commentImproved version, 12 pp

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Cited by in corpus (4)

• Geometric quantum discord of an arbitrary two-qudit state: the exact value and general upper bounds
• Nonviolation of the CHSH inequality under local spin-1 measurements on two spin qutrits
• Violation of Svetlichny's inequality in a system of spins $j$
• High-spin measurements in an arbitrary two-qudit state