Optimal measurements to access classical correlations of two-qubit states

TL;DR

This paper investigates the optimal measurements for accessing classical correlations in two-qubit states, revealing that a specific measurement type, the MCDM, is often optimal and can approximate quantum discord.

Contribution

It introduces the maximal-correlation-direction measurement (MCDM) as an optimal measurement for classical correlations in two-qubit states and provides bounds for quantum discord using MCDM.

Findings

MCDM is optimal for states with zero-discord and maximally mixed marginals.

The probability distribution of optimal measurements is centered around MCDM.

An upper bound for quantum discord based on MCDM is established.

Abstract

We analyze the optimal measurements accessing classical correlations in arbitrary two-qubit states. Two-qubit states can be transformed into the canonical forms via local unitary operations. For the canonical forms, we investigate the probability distribution of the optimal measurements. The probability distribution of the optimal measurement is found to be centralized in the vicinity of a specific von Neumann measurement, which we call the maximal-correlation-direction measurement (MCDM). We prove that for the states with zero-discord and maximally mixed marginals, the MCDM is the very optimal measurement. Furthermore, we give an upper bound of quantum discord based on the MCDM, and investigate its performance for approximating the quantum discord.