Entangler and analyzer for multiphoton Greenberger-Horne-Zeilinger states using weak nonlinearities

In the regime of weak nonlinearity we present two general, feasible schemes for manipulating photon states. One is an entangler for generating any one of the n-photon Greenberger-Horne-Zeilinger (GHZ) states. Interactions of the incoming photons with cross-Kerr media followed by a phase shift gate and a measurement on a probe beam plus appropriate local operations using classical feed-forward of the measurement results allow one to obtain the desired states in a nearly deterministic manner. The second scheme discussed is an analyzer for multiphoton maximally entangled states, which is derived from the above entangler. In this scheme, all of the 2nn-photon GHZ states can, nearly deterministically, be discriminated.