  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.
