On the Disentanglement of States

Disentanglement is the process which transforms a state $\rho$ of two subsystems into an unentangled state, while not effecting the reduced density matrices of each of the two subsystems. Recently Terno showed that an arbitrary state cannot be disentangled into a tensor product of its reduced density matrices. In this letter we present various novel results regarding disentanglement of states. Our main result is that there are sets of states which cannot be successfuly disentangled (not even into a separable state). Thus, we prove that a universal disentangling machine cannot exist.