On four-photon entanglement from parametric down-conversion process

We propose a scheme to generate a family of four-photon polarization-entangled states from the second-order emission of the spontaneous parametric down-conversion (PDC) process. Based on linear optical elements and the coincidence detection, the four indistinguishable photons emitted from PDC source result in the family of states which are so different from the previous. By tuning the orientation of wave plate, we are able to obtain the well-known four-photon Greenberger-Horne-Zeilinger (GHZ) state, superposition of two (three) orthogonal GHZ states and generic superposition of four orthogonal GHZ states. As an application, we analyze quantum nonlocality for the present superposition states. Under particular phase settings, we calculate the local hidden variable (LHV) correlation and the quantum correlation function. As a result, the Bell inequality derived from the LHV correlation is completely violated by these four-photon entangled states. The maximal quantum violation occurs naturally with the four-photon GHZ state, and there exist the quantum violations which are larger than previously reported values over a surprisingly wide range. It means that the present four-photon entangled states are therefore suitable for testing the LHV theory.