Characterization of distillable and activatable states using entanglement witnesses

We introduce a formalism that connects entanglement witnesses and the distillation and activation properties of a state. We apply this formalism to two cases: First, we rederive the results presented in Eggeling et al. (e-print quant-ph/0104095), namely, that one copy of any bipartite state with nonpositive partial transpose (NPPT) is either distillable, or activatable. Second, we show that there exist three-partite NPPT states, with the property that two copies can neither be distilled, nor activated