A new criteria for zero quantum discord

We propose a new criterion to judge zero quantum discord for arbitrary bipartite states. A bipartite quantum state has zero quantum discord if and only if all blocks of its density matrix are normal matrices and commute with each other. Given a bipartite state with zero quantum discord, how to find out the set of local projectors, which 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 to realize it. Consequently, we prove that the positive operator-valued measurement can not extinguish the quantum correlation of a bipartite state with nonzero quantum discord.