Correlation time expansion for multidimensional weakly non-markovian gaussian processes

Pietro Liuzzo-Scorpo, Wojciech Roga, Leonardo A. M. Souza +2 more

We investigate the dynamics of Gaussian states of continuous variable systems under Gaussianity-preserving channels. We introduce a hierarchy of such evolutions encompassing Markovian and weakly and strongly non-Markovian processes and provide simple criteria to distinguish between the classes, based on the degree of positivity of intermediate Gaussian maps. We present an intuitive classification of all one-mode Gaussian channels according to their non-Markovianity degree and show that weak non-Markovianity has an operational significance, as it leads to a temporary phase-insensitive amplification of Gaussian inputs beyond the fundamental quantum limit. Explicit examples and applications are discussed.

Rolf Gohm

Adrián A. Budini

We give a complete characterization of the stochastic wave formalism when color Gaussian fluctuations are assumed. It is shown that in this case there is only one possible generalization of the stochastic wave dynamics, which is given by the ``non-Markovian quantum state diffusion model'' [Phys. Rev. A 58, 1699 (1998)]. Using functional techniques, we found an equivalent evolution in terms of the stochastic propagator. From this equation any controlled approximation can be constructed. The mean density-matrix evolution is given in a closed form. A relation with quantum master equations is established. An interaction parameter expansion and a small correlation time expansion are developed.

Yazhen Wang

Xin Liu, Wei Wu

We investigate the time evolution of quantum correlations, which are measured by Gaussian quantum discord in a continuous-variable bipartite system subject to common and independent non-Markovian environments. Considering an initial two-mode Gaussian symmetric squeezed thermal state, we show that quantum correlations can be created during the non-Markovian evolution, which is different from the Markovian process. Furthermore, we find that the temperature is a key factor during the evolution in non-Markovian environments. For common reservoirs, a maximum creation of quantum correlations may occur under an appropriate temperature. For independent reservoirs, the non-Markovianity of the total system corresponds to the subsystem whose temperature is higher. In both common and independent environments, the Gaussian quantum discord is influenced by the temperature and the photon number of each mode.

Eduardo Souza Fraga, Gastão I. Krein, L. F. Palhares