Gaussification through decoherence

Abstract

We investigate the loss of nonclassicality and non-Gaussianity of a single-mode state of the radiation field in contact with a thermal reservoir. The damped density matrix for a Fock-diagonal input is written using the Weyl expansion of the density operator. Analysis of the evolution of the quasiprobability densities reveals the existence of two successive characteristic times of the reservoir which are sufficient to assure the positivity of the Wigner function and, respectively, of the $P$ representation. We examine the time evolution of non-Gaussianity using three recently introduced distance-type measures. They are based on the Hilbert-Schmidt metric, the relative entropy, and the Bures metric. Specifically, for an $M$-photon-added thermal state, we obtain a compact analytic formula of the time-dependent density matrix that is used to evaluate and compare the three non-Gaussianity measures. We find a good consistency of these measures on the sets of damped states. The explicit damped quasiprobability densities are shown to support our general findings regarding the loss of negativities of Wigner and $P$ functions during decoherence. Finally, we point out that Gaussification of the attenuated field mode is accompanied by a nonmonotonic evolution of the von Neumann entropy of its state conditioned by the initial value of the mean photon number.

Published version. Comments are welcome

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Cited by in corpus (7)

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• Two-mode Schrödinger-cat states with nonlinear optomechanics: generation and verification of non-Gaussian mechanical entanglement
• Loss of non-Gaussianity for damped photon-subtracted thermal states
• Quantum speed of evolution in a Markovian bosonic environment
• A trapped ion in an optical cavity: numerical study of an optomechanical transition in the few-photon regime
• Modification of polarization through de-Gaussification