Gaussification through decoherence

TL;DR

This paper studies how nonclassical and non-Gaussian features of a quantum optical state diminish over time due to interaction with a thermal reservoir, identifying characteristic times for the loss of quantum negativities and analyzing the process of Gaussification.

Contribution

It provides a detailed analysis of the decoherence process for non-Gaussian states, introducing analytic formulas and comparing multiple measures of non-Gaussianity during damping.

Findings

Positivity times for Wigner and P functions identified

Three non-Gaussianity measures show consistent results

Gaussification linked to nonmonotonic von Neumann entropy evolution

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.