  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.
