Geometric quantum discord for two-qubit X-states

TL;DR

This paper derives explicit formulas and bounds for the Bures distance of quantum discord in two-qubit X-states, enhancing the understanding of quantum correlations in this important class of states.

Contribution

It provides the first explicit expression for Bures distance of discord for a family of X-states and offers bounds for general two-qubit X-states.

Findings

Explicit formula for Bures distance of discord for a five-parameter family of X-states.

Calculated Bures distance of discord for a subset of X-states via optimal measurements.

Provided an analytic upper bound for the Bures distance of discord in all two-qubit X-states.

Abstract

Two-qubit X-state is a large class of quantum states which plays an important role in the quantification and dynamical study of quantum correlations. However, the corresponding quantification of quantum discord is still missing for bona fide discord measures, like original quantum discord, Bures distance of discord, and relative entropy of discord. In this paper, we consider the calculation of Bures distance of discord, which is a kind of correlation satisfying all criteria of a discord measure, for two-qubit X-states. Firstly, we derive an explicit expression for Bures distance of discord for a kind of five-parameters family of states. Moreover, for general two-qubit X-states, we not only calculate the Bures distance of discord for a subset of two-qubit X-states by classifying and analyzing the optimal local measurements and the optimal projection operators but also provide an analytic upper bound for the entirety.