Quantifying non-Markovianity of continuous variable Gaussian dynamical maps

TL;DR

This paper proposes a new measure for non-Markovianity in continuous variable quantum systems using fidelity, and applies it to analyze Gaussian channels like damping and Brownian motion.

Contribution

It introduces a fidelity-based non-Markovianity measure and evaluates it for key Gaussian channels, providing analytical and numerical solutions.

Findings

Fidelity-based measure effectively quantifies non-Markovianity.

Analytical solutions for coherent states are derived.

Numerical and approximate solutions for squeezed states are provided.

Abstract

We introduce a non-Markovianity measure for continuous variable open quantum systems based on the idea put forward in H.-P. Breuer et al., Phys. Rev. Lett.\textbf{103}, 210401 (2009), i.e., by quantifying the flow of information from the environment back to the open system. Instead of the trace distance we use here the fidelity to assess distinguishability of quantum states. We employ our measure to evaluate non-Markovianity of two paradigmatic Gaussian channels: the purely damping channel and the quantum Brownian motion channel with Ohmic environment. We consider different classes of Gaussian states and look for pairs of states maximizing the backflow of information. For coherent states we find simple analytical solutions, whereas for squeezed states we provide both exact numerical and approximate analytical solutions in the weak coupling limit.