Quasiprobability distributions and the analysis of the linear quantum channel with thermal noise

Abstract

The quasiprobability distributions (QPD) introduced by Cahill and Glauber much simplify calculating the density operator of the output of a linear quantum channel from the density operator of the input when the channel attenuates and is corrupted by thermal noise. This channel models, for instance, an attenuator viewed as a simple harmonic oscillator in contact with a heat bath, or the relation between the radiating field mode in the aperture of a transmitter and the field mode it excites at the aperture of a distant receiver. It is shown how the attenuation and the noise in the channel modify the dependence of the QPD on the ordering parameter s. The form of the QPD at the output indicates that the greater the attenuation, the more nearly the state of the output resembles a classical state. Indeed, the addition of thermal noise contributing on the average only one photon suffices to convert an arbitrary unimodal state into a classical state. The principal result of the paper is applied to determining the output of a quantum channel whose input mode is in a generalized coherent state.