ar X iv : q ua nt - p h / 01 10 01 1 v 1 1 O ct 2 00 1 General Entanglement Purification Protocols

We study the problem of general entanglement purification protocols: Alice and Bob share a bipartite state which is " reasonably close " to the perfect EPR pairs, and they wish to " purify " this share state by performing local operations and classical communication and outputting a state that can be arbitrarily close to EPR pairs, and the only information Alice and Bob have concerning the input state is the fidelity of the input state and the maximally entangled state. We first prove a negative result that on average, Alice and Bob cannot increase the fidelity of the input state significantly, if they only have the limited information. Next, we show several protocols that will fail with a small probability, but will output states arbitrarily close to EPR pairs with very high probability if they don't fail. We also present a protocol that very efficiently converts maximally entangled states into EPR pairs with optimal yield up to an additive constant. All our constructions are efficient, i.e., they can be implemented by polynomial-size quantum circuits.