Fast multi-copy entanglement purification with linear optics

We describe an entanglement purification protocol for a polarization Bell state. Different from the previous protocols, it does not require the controlled-not gate, and only uses linear optical elements to complete the task. This protocol requires multi-copy degraded mixed states, which can make this protocol obtain a high fidelity in one purification step. It can also be extended to purify the multi-photon Greenberger-Horne-Zeilinger (GHZ) state. This protocol may be useful in future long-distance communication.