Efficient single-photon entanglement concentration for quantum communications

Abstract: We present two protocols for the single-photon entanglement concentration. With the help of the 50:50 beam splitter, variable beam splitter and an auxiliary photon, we can concentrate a less-entangled single-photon state into a maximally single-photon entangled state with some probability. The first protocol is implemented with linear optics and the second protocol is implemented with the cross-Kerr nonlinearity. Our two protocols do not need two pairs of entangled states shared by the two parties, which makes our protocols more economic. Especially, in the second protocol, 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 our protocols useful in the long-distance quantum communication.