Non-commutativity measure of quantum discord

TL;DR

This paper introduces two new measures of quantum discord based on non-commutativity, which are easy to compute and effectively reflect the quantum correlations in various states.

Contribution

It proposes novel non-commutativity-based measures of quantum discord using trace and Hilbert-Schmidt norms, applicable to arbitrary-dimensional states.

Findings

Measures reflect the amount of quantum discord accurately.

Easy to calculate for states of any dimension.

Validated through several illustrative examples.

Abstract

Quantum discord is a manifestation of quantum correlations due to non-commutativity rather than entanglement. Two measures of quantum discord by the amount of non-commutativity via the trace norm and the Hilbert-Schmidt norm respectively are proposed in this paper. These two measures can be calculated easily for any state with arbitrary dimension. It is shown by several examples that these measures can reflect the amount of the original quantum discord.