  We propose a nonlocal entanglement concentration protocol (ECP) for
$N$-photon systems in a partially entangled W state, resorting to some
ancillary single photons and the parity-check measurement based on cross-Kerr
nonlinearity. One party in quantum communication first performs a parity-check
measurement on her photon in an $N$-photon system and an ancillary photon, and
then she picks up the even-parity instance for obtaining the standard W state.
When she obtains an odd-parity instance, the system is in a less-entanglement
state and it is the resource in the next round of entanglement concentration.
By iterating the entanglement concentration process several times, the present
ECP has the total success probability approaching to the limit in theory. The
present ECP has the advantage of a high success probability. Moreover, the
present ECP requires only the $N$-photon system itself and some ancillary
single photons, not two copies of the systems, which decreases the difficulty
of its implementation largely in experiment. It maybe have good applications in
quantum communication in future.
