Weak quantum discord

TL;DR

This paper introduces weak quantum discord, a measure of quantum correlations that accounts for weak measurements, resolving a paradox about its behavior compared to projective measurements.

Contribution

It defines and interprets weak quantum discord, including a symmetric version, providing new insights into quantum correlations under weak measurements.

Findings

Weak measurements can yield higher quantum discord values than projective measurements.

The paper introduces a new quantifier for weak quantum discord.

A symmetric version of weak quantum discord is proposed.

Abstract

Originally introduced as the difference between two possible forms of quantum mutual information, quantum discord has posteriorly been shown to admit a formulation according to which it measures a distance between the state under scrutiny and the closest projectively measured (non-discordant) state. Recently, it has been shown that quantum discord results in higher values when projective measurements are substituted by weak measurements. This sounds paradoxical since weaker measurements should imply weaker disturbance and, thus, a smaller distance. In this work we solve this puzzle by presenting a quantifier and an underlying interpretation for what we call weak quantum discord. As a by-product, we introduce the notion of symmetrical weak quantum discord.