Comparison of quantum discord and relative entropy in some bipartite quantum systems

TL;DR

This paper compares quantum discord and relative entropy as measures of quantum correlations in bipartite systems, establishing their equivalence for certain states and providing examples with X-states.

Contribution

It introduces a relation between quantum discord and relative entropy, showing their equality for symmetrical X-states and illustrating with specific bipartite examples.

Findings

Quantum discord equals relative entropy for symmetrical X-states.

Relative entropy can serve as a measure of quantum correlations.

Examples include two-qubit and qubit-qutrit systems.

Abstract

The study of quantum correlations in High-dimensional bipartite systems is crucial for the development of quantum computing. We propose relative entropy as a distance measure of correlations may be measured by means of the distance from the quantum state to the closest classical-classical state. In particular, We establish relations between relative entropy and quantum discord quantifiers obtained by means of orthogonal projective measurements. We show that for symmetrical X-states density matrices the quantum discord is equal to relative entropy. At the end of paper, various examples of X-states such as two-qubit and qubit-qutrit have been demonstrated .