Quantum discord, a measure of quantum correlation beyond entanglement, is initially defined as the discord between two classically equivalent while quantum discordant definitions of mutual information. In this paper, we report some new interpretations of discord which rely on the differences between measurement induced effects on the local measured system and the whole system. Specifically, with proper quantitative definitions introduced in [Buscemi, Hayashi and Horodecki, Phys. Rev. Lett. 100, 2210504 (2008)], we find that quantum discord can be interpreted as the differences of measurement induced disturbance or information gain on the local measured system and on the whole system. Combined with previous similar results based on measurement induced entanglement and decoherence, our results provide a unified view on quantum discord.

title changed, abstract rewritten. Rank-1 POVM measurements are needed for our results