Entangler and analyzer for multiphoton maximally entangled states using weak nonlinearities

In the regime of weak nonlinearity we present two general feasible schemes. One is an entangler for generating any one of the $n$-photon Greenberger-Horne-Zeilinge (GHZ) states and Bell states. After the interactions with cross-Kerr nonlinear media, a phase gate followed by a measurement on the probe beam, and appropriate local operations via classical feed-forward, one can obtain the desired states in a nearly deterministic way. Another scheme is an analyzer for multiphoton maximally entangled states, which is taken as a further application of the above entangler. In this scheme, all of the $2^n$ $n$-photon GHZ states can, nearly deterministically, be discriminated. Furthermore, an efficient two-step nondestructive Bell-state analyzer is designed.