Analytical Expression of Quantum Discord for Rank-2 Two-qubit States

TL;DR

This paper derives explicit analytical formulas for quantum discord in rank-2 two-qubit states, enhancing understanding of quantum correlations in quantum information processing.

Contribution

It provides the first analytical expressions for quantum discord in rank-2 two-qubit states, linking classical correlations and quantum discord.

Findings

Analytical formula for linear entropy based classical correlation in $d\otimes 2$ states

Explicit formula for von Neumann entropy based classical correlation in rank-2 two-qubit states

Derived an explicit expression for quantum discord in rank-2 two-qubit states

Abstract

Quantum correlations characterized by quantum entanglement and quantum discord play important roles in many quantum information processing. We study the relations among the entanglement of formation, concurrence, tangle, linear entropy based classical correlation and von Neumann entropy based classical correlation. We present analytical formulae of linear entropy based classical correlation for arbitrary $d\otimes 2$ quantum states and von Neumann entropy based classical correlation for arbitrary $2\otimes 2$ rank-2 quantum states. From the von Neumann entropy based classical correlation, we derive an explicit formula of quantum discord for arbitrary rank-2 two-qubit quantum states.