Quantum discord of two-qubit X-states

TL;DR

This paper analyzes quantum discord in two-qubit X-states, identifying classes where it can be computed analytically and illustrating the limitations of existing algorithms, thereby clarifying the nature of quantum correlations.

Contribution

It identifies classes of X-states with analytically computable quantum discord and highlights the limitations of a recent algorithm, revealing differences between measurement types.

Findings

Certain X-states allow analytical quantum discord calculation without minimization.

The existing algorithm fails for a specific family of X-states.

Explicit example showing inequivalence between measurement minimizations.

Abstract

Quantum discord provides a measure for quantifying quantum correlations beyond entanglement and is very hard to compute even for two-qubit states because of the minimization over all possible measurements. Recently a simple algorithm to evaluate the quantum discord for two-qubit X-states is proposed by Ali, Rau and Alber [Phys. Rev. A 81, 042105 (2010)] with minimization taken over only a few cases. Here we shall at first identify a class of X-states, whose quantum discord can be evaluated analytically without any minimization, for which their algorithm is valid, and also identify a family of X-states for which their algorithm fails. And then we demonstrate that this special family of X-states provides furthermore an explicit example for the inequivalence between the minimization over positive operator-valued measures and that over von Neumann measurements.