Catalysis of entanglement manipulation for mixed states

We consider entanglement-assisted remote quantum state manipulation of bipa rtite mixed states. Several aspects are addressed: we present a class of mi xed states of rank two that can be transformed into another class of mixed stales under entanglement-assisted local operations with classical communic ation, but for which such a transformation is impossible without assistance . Furthermore, we demonstrate enhancement of the efficiency of purification protocols with the help of entanglement-assisted operations. Finally, tran sformations from one mixed state to mixed target states which are sufficien tly close to the source state are contrasted with similar transformations i n the pure-state case.