Efficient single-photon entanglement concentration for quantum communications

We present two entanglement concentration protocols for single-photon entanglement. The first protocol is implemented with linear optics. With the help of the 50:50 beam splitter, variable beam splitter and an auxiliary photon, a less-entangled single-photon state can be concentrated into a maximally single-photon entangled state with some probability. The second protocol is implemented with the cross-Kerr nonlinearity. With the help of the cross-Kerr nonlinearity, the sophisticated single photon detector is not required. Moreover, the second protocol can be reused to get higher success probability. All these advantages may make the protocols useful in the long-distance quantum communication.