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'-photon subsystems (2 \leq N'<N) coming from the
instances which are just discarded in all existing conventional MEPPs. The
entangled N'-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.Comment: 17 pages, 9 figures, 2 tables. We correct the error in the address of
the author in the published version (Phys. Rev. A 84, 052312 (2011)
