Entanglement concentration for arbitrary unknown less-entangled three-photon W states with linear optics

We present two three-photon entanglement concentration protocols (ECPs) for an arbitrary unknown less-entangled W-class state, resorting to linear optical elements. In our normal ECP, the three parties can obtain a three-photon system in a standard W state probabilistically, similar to the Schmidt projection method. In our improved ECP, the parties obtain not only some higher-fidelity partially entangled three-photon systems but also some entangled two-photon systems in each round of concentration with two copies of three-photon systems. It is interesting to show that the three-photon and two-photon systems kept after a round of concentration have the same parameters. The parties can obtain some three-photon systems in a standard W state with a far higher success probability than the normal ECP, by exploiting the three-photon and two-photon systems with the same parameters as the resource for the next round of concentration. Both of these ECPs may have good applications in quantum communication in the future.