Complete Bell-state and Greenberger-Horne-Zeilinger-state nondestructive detection based on simplified symmetry analyzer

We present a simplified symmetry analyzer (SA) with cross-Kerr nonlinearity, quantum non-demolition photon number measurement and basic optical elements. Based on the present symmetry analyzer (SA), all the Bell states can be discriminated nondestructively with nearly unity probability. In addition, with the help of cross-phase modulation (XPM) induced by giant cross-Kerr nonlinearity, three-photon Greenberger-Horne-Zeilinger (GHZ) state can also be discriminated determinately and nondestructively, which is supposed to be meaningful in quantum information processing.