Geometric picture of quantum discord for two-qubit quantum states

TL;DR

This paper introduces a geometric approach to understanding quantum discord in two-qubit states, extending it beyond X states to more general states, and providing insights into their classical and quantum correlations.

Contribution

It presents a novel geometric framework for quantum discord, applicable to general two-qubit states, and offers analytical and numerical insights into their correlations.

Findings

Geometric interpretation of quantum discord for X states.

Extension of geometric method to more general states.

Analytical expressions for correlations in some cases.

Abstract

Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find analytical expression of quantum discord is an intractable task. Exact results are known only for very special states, namely, two-qubit X-shaped states. We present in this paper a geometric viewpoint, from which two-qubit quantum discord can be described clearly. The known results about X state discord are restated in the directly perceivable geometric language. As a consequence, the dynamics of classical correlations and quantum discord for an X state in the presence of decoherence is endowed with geometric interpretation. More importantly, we extend the geometric method to the case of more general states, for which numerical as well as analytica results about quantum discord have not been found yet. Based on the support of numerical computations, some conjectures are proposed to help us establish geometric picture. We find that the geometric picture for these states has intimate relationship with that for X states. Thereby in some cases analytical expressions of classical correlations and quantum discord can be obtained.