nt - p h / 02 07 11 4 v 1 1 9 Ju l 2 00 2 1 Non - classical Gaussian states in noisy environ - ments

Research in the field of quantum information theory nowadays focusses more and more on the possibilities of practical implementation of quantum information processes. One of the most promising attempts has seemed to be the usage of entangled Gaussian states since they are rather easy to produce with optical means. In this article we will review properties of Gaussian states and describe operations on them. The interaction of the electromagnetic field with an absorbing dielectric as a special type of environmental interaction will serve as the basis for the understanding of decoherence and entanglement degradation of Gaussian states of light propagating through fibers. In Section 1.2 we shortly review the definition of Gaussian states and operations that can be performed on them. These includes symplectic (unitary) transformations, trace-preserving maps, and projective measurements. The important definitions of classicality, separability, and entanglement are defined and appropriate measures are given for them. In Section 1.3 we review some results on entanglement degradation in dielectric environments. We discuss the decoherence of Gaussian quantum states of light transmitted through absorbing dielectric objects such as fibers. Section 1.4 is devoted to the study of quantum teleportation in noisy environments. Special emphasis is put onto the question of choosing the correct displacement on the receiver’s side.