Paulina Marian, Iulia Ghiu, Tudor A. Marian
We investigate the time evolution of three recently introduced distance-type measures of non-Gaussianity for one-mode states of a radiation field in contact with a thermal reservoir. They are based on the Hilbert-Schmidt metric, relative entropy and Bures metric. We first write the damped density matrix for an input Fock-diagonal state using the Weyl expansion of the density operator. 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 the examined measures on the sets of damped states. Finally, we show that gaussification of the attenuated field mode is accompanied by a non-monotonic evolution of the von Neumann entropy of its state conditioned by the initial value of the mean photon number.
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http://arxiv.org/abs/1211.1701
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