Quantum discord of two-qubit rank-two states

TL;DR

This paper derives an analytical expression for quantum discord in two-qubit rank-two states using Koashi-Winter relation and visualizes it with quantum steering ellipsoids, highlighting the optimal measurement strategies.

Contribution

It provides the first analytical formula for quantum discord in two-qubit rank-two states and discusses measurement optimality, expanding understanding of quantum correlations.

Findings

Analytical expression for quantum discord in rank-two states obtained.

Von Neumann measurement is optimal for rank-two states.

Three-element POVM measurement can be more optimal for higher-rank states.

Abstract

Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find analytical expression of quantum discord is an intractable task. In this paper, we discuss thoroughly the case of two-qubit rank-two states. An analytical expression for the quantum discord is obtained by means of Koashi-Winter relation. A geometric picture is demonstrated by means of quantum steering ellipsoid. We point out that in this case the optimal measurement is indeed the von Neumann measurement, which is usually used in the study of quantum discord. However, for some two-qubit states with the rank larger than two, we find that three-element POVM measurement is more optimal. It means that more careful attention should be paid in the discussion of quantum discord.