We consider how to teleport two- and three-mode Einstein-Podolsky Rosen entangled states （｜η） and ｜Pt, X2, X3）） via a ｜Pt, X2, X3） quantum channel for continuous variables. Using the complete and orthogonal representation of the entangled states, we can not only find the a complete basis set for the joint measurement but also propose the specific scheme of teleportation. Our calculation can be greatly simplified by using their Schmidt decompositions.
By introducing the entangled Fresnel operator （EFO） this paper demonstrates that there exists ABCD theorem for two-mode entangled case in quantum optics. The canonical operator method as mapping of ray-transfer ABCD matrix is explicitly shown by EFO＇s normally ordered expansion through the coherent state representation and the technique of integration within an ordered product of operators.
1. Introduction In quantum optics, optical frequency conversion is a typical nonlinear process and is worth studying, for example, a second harmonic frequency generation will generate a squeezed state.[1＇2l In this work, we tackle the evolution of an initial coherent state in a Raman dispersion process which is also a nonlinear process. The process involves the inelastic scattering of a pho- ton when it is incident on a molecule. The photon loses some of its energy to the molecule or gains some from it, and so leaves the molecule with a lower or a higher frequency. The lower frequency components of the scattered radiation are called the Stokes lines and the higher frequency components are called the anti- Stokes lines. The Hamiltonian governing its dynamics is[3]
