Dynamical paths and universality in continuous variables open systems

TL;DR

This paper investigates the universal behavior of quantum correlations in continuous variable open systems, revealing that dynamical paths depend only on initial states and environmental temperature, with implications for simplifying the analysis of non-Markovian processes.

Contribution

It introduces the concept of universal dynamical paths in Gaussian states and demonstrates their dependence solely on initial conditions and environment temperature, unifying Markovian and non-Markovian dynamics.

Findings

Dynamical paths are universal, depending only on initial states and environmental temperature.

Non-Markovian effects are reflected in the velocity along these paths.

Identifies regions in parameter space that cannot be connected by Gaussian dynamical maps.

Abstract

We address the dynamics of quantum correlations in continuous variable open systems and analyze the evolution of bipartite Gaussian states in independent noisy channels. In particular, upon introducing the notion of dynamical path through a suitable parametrization for symmetric states, we focus attention on phenomena that are common to Markovian and non-Markovian Gaussian maps under the assumptions of weak coupling and secular approximation. We found that the dynamical paths in the parameter space are universal, that is they do depend only on the initial state and on the effective temperature of the environment, with non Markovianity that manifests itself in the velocity of running over a given path. This phenomenon allows one to map non-Markovian processes onto Markovian ones and it may reduce the number of parameters needed to study a dynamical process, e.g. it may be exploited to build constants of motions valid for both Markovian and non-Markovian maps. Universality is also observed in the value of Gaussian discord at the separability threshold, which itself is a function of the sole initial conditions in the limit of high temperature. We also prove the existence of excluded regions in the parameter space, i.e. of sets of states which cannot be linked by any Gaussian dynamical map.