Scheme for generating a long-distance two-photon entangled state in a noisy channel via time-bin encoding and decoding

A scheme is proposed for generating a long-distance two-photon entangled state in a noisy channel with the help of a cross-Kerr medium and photon number measurement via time-bin encoding and decoding. In the scheme, the influence of the noise can be eliminated effectively through time-bin encoding and decoding, the photon number detector is used to distinguish vacuum and nonvacuum states, and the minus conditional phase shift is not required. The method is also useful in other types of large-scale and long-distance quantum information processing via noisy channels.