Se p 19 98 Sending quantum information with Gaussian states

1 Information characteristics of a quantum channel During the last couple of years an impressive progress has been achieved in the theory of transmission of classical information through quantum communication channels (see [8] for a comprehensive survey). The problem of sending quantum information is much less understood; we refer in particular to the papers [10], [2], [1], initiating the study of this problem, where the reader can find further references. In this paper we make a contribution to this study by considering rather concrete situation: sending Gaussian (quasifree) states through linear Bosonic channels. Consider quantum system in a Hilbert space H, with a fixed density operator ρ. A channel is a transformation of quantum states as presented by density operators, given by the relation T [ρ] = j A j ρA * j , where A j are bounded operators in H satisfying j A * j A j = I. Let us denote H(ρ) = −Trρ log ρ the von Neumann entropy of a density operator ρ. We call ρ the input state, and T [ρ] the output state of the channel. There are three important entropy quantities related to the couple (ρ, T) : 1) The entropy of the input state H(ρ); 2) The entropy of the output state H(T [ρ]); 3) The entropy exchange H(ρ, T).