Bell violation versus geometric measure of quantum discord and their dynamical behavior

TL;DR

This paper explores the relationship between Bell inequality violations and geometric quantum discord in two-qubit systems, providing bounds and analyzing their behavior under various decoherence environments.

Contribution

It derives exact bounds for Bell violation versus geometric discord for Bell diagonal states and analyzes their dynamical behavior under different decoherence models.

Findings

Bell violation closely relates to geometric discord.

Bounds are characterized for Bell diagonal states.

Dynamical behavior varies with decoherence type.

Abstract

Motivated by recent numerous works on the interplay among various measures of quantum correlations, we aim to investigate the relationship between the violation of Clauser-Horne-Shimony-Holt (CHSH) Bell inequality and geometric measure of quantum discord for two-qubit systems. Exact lower and upper bounds of Bell violation versus geometric discord are obtained for a specific and significant class of states, Bell diagonal states, and the respective states which suffice those bounds are also characterized. The dynamical behavior of these two quantifiers is carefully analyzed in the presence of decoherence, including Markovian, non-Markovian, and non-back-action quantum environments. The results suggest that Bell violation is closely related to geometric discord, like its relationship with other entanglement monotones.