 Positive-map separability criterion

A finite-dimensional bipartite density operator ${\rho }_{AB}$ is a separable quantum state exactly when $({\mathrm{id}}_A\otimes \Phi )({\rho }_{AB})\ge 0$ for every positive linear map from operators on $B$ to operators on $A$. In combination with the Størmer-Woronowicz decomposability theorem, it makes the positive partial transpose criterion sufficient for qubit-qutrit states. The criterion is established in the Horodeckis' separability paper.