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.

Improved version, 12 pp

References in corpus (5)

• Concurrence of arbitrary dimensional bipartite quantum states
• Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity
• Semi-device-independent bounds on entanglement
• The Bloch vectors formalism for a finite-dimensional quantum system
• Specifying nonlocality of a pure bipartite state and analytical relations between measures for bipartite nonlocality and entanglement

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