Scheme for generating GHZ-type and W-type entangled squeezed vacuum states in free-travelling optical fields

We propose two schemes to generate GHZ-type and W-type entangled squeezed vacuum states with free-travelling optical fields via a single-photon source, the Kerr medium, balanced beam-splitters and single-photon detectors. The effects of a fluctuation of nonlinear phase shift between two optical fields on the fidelity and on the success probability are discussed. We also discuss the effects of the imperfection of photon detectors on the success probability and the experimental feasibility of the present schemes.