ABCD law of two-mode Gaussian-entangled light fields in linear optical systems

In this paper, we have theoretically investigated the propagation of two-mode Gaussian-entangled light fields (TGLFs) passing through a linear optical system. A general transformation formula of the TGLFs passing through the linear optical system has been derived under the paraxial approximation. Based on the derived formula, we have illustrated two typical examples: in the first example, the Einstein–Podolsky–Rosen (EPR) correlation of TGLFs propagating in a free space depends on the propagation distance and its value increases greatly with the propagation distance. In the second example, it is shown that the EPR correlation can be manipulated and controlled in the lens system. Moreover, we find that the von Neumann entropy of TGLFs does not change when TGLFs travel in these linear optical systems, verifying the entanglement of TGLFs is an intrinsic property. Our results may have potential applications in the first-order linear optical systems of quantum communication systems.