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.
We present two economical one-step error-correction protocols for multipartite polarization-entangled systems in a Greenberger-Horne-Zeilinger state. One uses spatial entanglement to correct errors in the polarization entanglement of an
N-photon system, resorting to linear optical elements. The other uses frequency entanglement to correct errors in the polarization entanglement of an
N-photon system. The parties in quantum communication can obtain a maximally entangled state from each
N-photon system transmitted with one step in these two protocols, and both of their success probabilities are
100, in principle. That is, they both work in a deterministic way, and they do not largely consume the less-entangled photon systems, which is far different from conventional multipartite entanglement purification schemes. These features may make these two protocols more useful for practical applications in long-distance quantum communication.