Optimal entanglement concentration for three-photon W states with parity check measurement

We present an efficient entanglement concentration protocol (ECP) for the less-entangled W state with some same conventional polarized single photons. In the protocol, two of the parties say Alice and Charlie should perform the parity check measurements and they can ultimately obtain the maximally entangled W state with a certain success probability. Otherwise, they can obtain another less-entangled W state, which can be reconcentrated into the maximally entangled W state. By iterating this ECP, a high success probability can be achieved. This ECP may be an optimal one and it is useful in current quantum information processing.