Quantum optical ABCD theorem in two-mode case

By introducing the entangled Fresnel operator (EFO) this paperdemonstrates that there exists ABCD theorem for two-mode entangledcase in quantum optics. The canonical operator method as mapping ofray-transfer ABCD matrix is explicitly shown by EFO's normallyordered expansion through the coherent state representation and thetechnique of integration within an ordered product of operators.