On the optimal measurement for quantum discord of two-qubit states

TL;DR

This paper introduces an efficient method for exactly calculating quantum discord in two-qubit X states, clarifies measurement optimality using a geometric approach, and identifies conditions where specific measurements are optimal.

Contribution

It provides a precise solution for quantum discord in two-qubit X states and clarifies measurement optimality with a geometric perspective.

Findings

Either von Neumann or three-element POVM measurements are optimal.

Postmeasurement ensemble components are invariant for certain states.

The method simplifies quantum discord calculation for two-qubit X states.

Abstract

We present an efficient method to solve the quantum discord of two-qubit X states exactly. A geometric picture is used to clarify whether and when the general POVM measurement is superior to von Neumann measurement. We show that either the von Neumann measurement or the three-element POVM measurement is optimal, and more interestingly, in the latter case the components of the postmeasurement ensemble are invariant for a class of states.