A new kind of tripartite entangled state representation in Fock space

We construct a tripartite entangled sate representation in Fock space, which is the eigenstate of the three compatible operators (Q1 − Q3), (Q1 + Q2 + Q3) and (P1 − 2P2 + P3). Using the technique of integration within an ordered product (IWOP) of operators, we show that |p, χ1, χ2〉 are complete and orthogonal, and hereby qualified for making up a quantum mechanical representation. Its squeezing property is explored and an optical device for producing this three-mode entangled state are proposed.