We present an efficient multipartite entanglement purification protocol (MEPP) for $N$-photon systems in a Greenberger-Horne-Zeilinger state with parity-check detectors. It contains two parts. One is the conventional MEPP with which the parties can obtain a high-fidelity $N$-photon ensemble directly, similar to the MEPP with controlled-not gates. The other is our recycling MEPP in which the entanglement link is used to produce some $N$-photon entangled systems from entangled $N^{\prime }$-photon subsystems ($2⩽N^{\prime }<N$) coming from the instances which are just discarded in all existing conventional MEPPs. The entangled $N^{\prime }$-photon subsystems are obtained efficiently by measuring the photons with potential bit-flip errors. With these two parts, the present MEPP has a higher efficiency than all other conventional MEPPs.

• Received 6 September 2011
• Corrected 19 December 2011

DOI:https://doi.org/10.1103/PhysRevA.84.052312