A new criterion for zero quantum discord

We propose a new criterion for judging zero quantum discord for arbitrary bipartite states. A bipartite quantum state has zero quantum discord if and only if all the blocks of its density matrix are normal matrices and commute with each other. Given a bipartite state with zero quantum discord, the question of how to find the set of local projectors that do not disturb the whole state after being imposed on one subsystem is also presented. A class of two-qubit X-state is used to test the criterion, and an experimental scheme is proposed for realizing it. Consequently, we prove that the positive operator-valued measurement cannot extinguish the quantum correlation of a bipartite state with nonzero quantum discord.