Highly efficient scheme for the preparation of four-photon polarization entangled state via quantum non-demolition measurement with classical feed-forward

A simple and efficient scheme is proposed to prepare a four-photon entangled state, which can be used as a resource for realizing a controlled-NOT (CNOT) gate pointed out by Gottesman and Chuang [Nature 402 (1999) 390], with the help of the cross-Kerr nonlinearity. The distinct feature of the present scheme is its preparation with near unity success probability and near perfect fidelity. It is not necessary in the present scheme that the cross-Kerr nonlinearity is very large because the weak nonlinearity can be compensated by using a coherent light laser probe beam with very large amplitude. This makes us more confident in the feasibility of the proposed scheme.