  We present an efficient and general multipartite entanglement purification
protocol (MEPP) for N-photon systems in Greenberger-Horne-Zeilinger (GHZ)
states with non-identical input states. As a branch of entanglement
purification, besides the cases of successful purification, the recurrence MEPP
actually has the reusable discarded items which are usually regarded as a
failure. Our protocol contains two parts for bit-flip error correction. The
first one is the conventional MEPP, corresponding successful cases. The second
one includes two efficient approaches, recycling purification with entanglement
link and direct residual entanglement purification, that can utilize discarded
items. We also make a comparison between two approaches. Which method to use
depends on initial input states, and in most cases the approach of direct
residual purification is optimal for it not only may obtain a higher fidelity
entangled state but also it does not require additional sophisticated links. In
addition, for phase-flip errors, the discarded items still have available
residual entanglement in the case of different input states. With these
approaches, this MEPP has a higher efficiency than all previous MEPPs and it
may have potential applications in the future long-distance quantum
communications and networks.
