Bipartite states with vanishing quantum discord are necessarily separable and hence positive partial transpose (PPT). We show that $2\times N$ 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 strong PPT (SPPT). Therefore, we provide a natural witness for a quantum discord: if a $2\times N$ 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.

• Received 8 April 2010

DOI:https://doi.org/10.1103/PhysRevA.81.062102