An economic and feasible scheme to generate the four-photon entangled state via weak cross-Kerr nonlinearity

We propose a novel scheme to generate four-photon polarization-entangled state with homodyne measurement via weak cross-Kerr nonlinearity. Compared with the former protocols, our protocol is more economic because we only use two weak cross-Kerr nonlinearities, and more feasible because we do not need minus conditional phase shift. All these advantages make our protocol more useful in quantum information processing.