Generation of three-photon polarization-entangled GHZ state via linear optics and weak cross-Kerr nonlinearity

We propose a simple scheme for generating three-photon polarization-entangled GHZ state via cross-Kerr medium, linear optical elements and P homodyne measurement. In our protocol, the two-photon interference is used rather than the single-photon interference, which decreases the difficulty in experimental realization. Besides, the generation scheme proposed doubles the phase shift θ, which will result in lower error probability and decoherence effect. These advantages make our scheme more feasible in the regime of weak cross-Kerr nonlinearity with current experimental technologies. In addition, we give two efficient schemes for the generation of arbitrary multi-photon GHZ state, which is significant to large-scale quantum information processing (QIP).