Quantum discord for two-qubit X-states

TL;DR

This paper derives explicit formulas for quantum discord in a broad class of two-qubit X-states, expanding understanding of quantum correlations beyond entanglement and their applications in quantum information.

Contribution

It provides the first explicit expressions for quantum discord in a seven-parameter family of two-qubit X-states, enhancing analytical tools for quantum correlation analysis.

Findings

Quantum discord can be explicitly calculated for X-states.

Quantum discord, classical correlation, and entanglement are independent measures.

No simple ordering exists among different quantum correlation measures.

Abstract

Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. In general, this correlation is different from entanglement, and quantum discord may be nonzero even for certain separable states. Even in the simple case of bipartite quantum systems, this different kind of quantum correlation has interesting and significant applications in quantum information processing. So far, quantum discord has been calculated explicitly only for a rather limited set of two-qubit quantum states and expressions for more general quantum states are not known. In this paper, we derive explicit expressions for quantum discord for a larger class of two-qubit states, namely, a seven-parameter family of so called X-states that have been of interest in a variety of contexts in the field. We also study the relation between quantum discord, classical correlation, and entanglement for a number of two-qubit states to demonstrate that they are independent measures of correlation with no simple relative ordering between them.