Linear And Nonlinear Multipartite Entangled State Representation

First, we introduce EPR entangled state in Fock space. The completeness relation and non-orthonormal property of such states are proven. Second, it is spreaded to multipartite entanglement, we have shown the completeness relation and non-orthonormal property of such multipartite entangled states.The scheme to generate these state are presented by combining a symmetrical beamsplitter, a parametric down-conversion and a polarizer. we consider an application of the entangled state in quantum squeezing theory,optical phase operator theory and quantum teleportation. Lastly, kinds of nonlinear multipartite entanglement are shown, and its applications are also discussed.