Weak quantum discord

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.