Local unambiguous discrimination with remaining entanglement

A bipartite state, which is secretly chosen from a finite set of known entangled pure states, cannot immediately be useful in standard quantum information processing tasks. To effectively make use of the entanglement contained in this unknown state, we introduce a way to locally manipulate the original quantum system: either identify the state successfully or distill some pure entanglement. Remarkably, if many copies are available, we show that any finite set of entangled pure states, whether orthogonal or not, can be locally distinguished in this way, which further implies that pure entanglement can be deterministically extracted from unknown entanglement. These results make it clear why a large class of entangled bipartite quantum operations including unitary operations and measurements that are globally distinguishable can also be locally distinguishable: They can generate pure entanglement consistently.