  Multipartite entanglement plays an important role in controlled quantum
teleportation, quantum secret sharing, quantum metrology and some other
important quantum information branches. However, the maximally multipartite
entangled state will degrade into the mixed state because of the noise. We
present an efficient multipartite entanglement purification protocol (EPP)
which can distill the high quality entangled states from low quality entangled
states for N-photon systems in a Greenberger-Horne-Zeilinger (GHZ) state in
only linear optics. After performing the protocol, the spatial-mode
entanglement is used to purify the polarization entanglement and one pair of
high quality polarization entangled state will be obtained. This EPP has
several advantages. Firstly, with the same purification success probability,
this EPP only requires one pair of multipartite GHZ state, while existing EPPs
usually require two pairs of multipartite GHZ state. Secondly, if consider the
practical transmission and detector efficiency, this EPP may be extremely
useful for the ratio of purification efficiency is increased rapidly with both
the number of photons and the transmission distance. Thirdly, this protocol
requires linear optics and does not add additional measurement operations, so
that it is feasible for experiment. All these advantages will make this
protocol have potential application for future quantum information processing.
