Evolution of twin-beam in active optical media

Abstract. We study the evolution of twin-beam propagating inside active media that may be used to establish a continuous variable entangled channel between two distant users. In particular, we analyze how entanglement is degraded during propagation, and determine a threshold value for the interaction time, above which the state become separable, and thus useless for entanglement based manipulations. We explicitly calculate the fidelity for coherent state teleportation and show that it is larger than one half for the whole range of parameters preserving entanglemenent. The crucial ingredient of quantum information is entanglement, which is the essential resource for quantum computing, teleportation, and cryptographic protocols. Entanglement is known to to be a valuable resource for improving measurements [1], spectroscopy [2, 3], lithography [4], interferometry [5], and tomography of quantum devices [6]. Most of these concepts were initially developed for discrete quantum variables, in particular quantum bits. Recently, however, much attention has been devoted to the use of continuous variables (CV), especially Gaussian state of light by means of linear optical circuits [7], since CV may be easier to manipulate than quantum bits in order to perform various information processes [8]. In the optical implementation of quantum information processing, the most relevant entangled channel is provided by the the twin-beam state (also called two-mode squeezed vacuum) of two modes of radiation, which, in the Fock bases, is expressed a