  Bipartite states with vanishing quantum discord are necessarily separable and
hence positive partial transpose (PPT). We show that 2 x N states satisfy
additional property: the positivity of their partial transposition is
recognized with respect to the canonical factorization of the original density
operator. We call such states SPPT (for strong PPT). Therefore, we provide a
natural witness for a quantum discord: if a 2 x N state is not SPPT it must
contain nonclassical correlations measured by quantum discord. It is an analog
of the celebrated Peres-Horodecki criterion: if a state is not PPT it must be
entangled.
