Reduction criterion of separability and limits for a class of distillationprotocols

We analyze the problem of distillation of entanglement of mixed states in h igher-dimensional compound systems. Employing the positive maps method [M. Horodecki et al., Phys. Lett. A 223, 1 (1996)] we introduce and analyze a c riterion of separability that relates the structures of the total density m atrix and its reductions. We show that any state violating the criterion ca n be distilled by suitable generalization of the two-qubit protocol that di stills any inseparable two-qubit state. In particular, this means that any state rho of two N-level systems with <psi(+)\rho\psi(+)> >1/N can be disti lled (psi(+) is the singlet state generalized to higher dimension). The cri terion also singles out all the states that can be distilled by a class of protocols. The proof involves construction of the family of states that are invariant under transformation rho-->UxU*rho U(dagger)xU*(dagger), where I is a unitary transformation and the asterisk denotes complex conjugation. The states are related to the depolarizing channel generalized to the nonbi nary case. [S1050-2947(99)05904-1].