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

Journal of Physics A: Mathematical and Theoretical. 2024. Vol. 57. No. 5. Article 055302.

Elena R. Loubenets, Sergey Kuznetsov, Louis Hanotel

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.

Keywords: quantum information, quantum correlations, quantum entanglement

Publication based on the results of: Methods of mathematical modeling of actual physical processes (2023)