Exploiting Gaussian steering to probe non-Markovianity due to the interaction with a structured environment

TL;DR

This paper introduces a Gaussian steering-based measure to quantify non-Markovianity in continuous-variable quantum channels, revealing how different environmental spectral densities influence quantum correlations and system dynamics.

Contribution

It proposes a novel measure based on Gaussian steering for non-Markovianity, applied to quantum Brownian motion channels with various environments, enhancing understanding of quantum correlations in non-Markovian processes.

Findings

Sub-Ohmic, high-temperature environments induce strong non-Markovianity.

Cyclic backflows of Gaussian steerability observed in certain environments.

The measure can be experimentally implemented to assess non-Markovianity.

Abstract

We put forward a measure based on Gaussian steering to quantify the non-Markovianity of continuous-variable (CV) Gaussian quantum channels. We employ the proposed measure to assess and compare the non-Markovianity of a quantum Brownian motion (QBM) channel, originating from the interaction with Ohmic and sub-Ohmic environments with spectral densities described by a Lorentz-Drude cutoff, both at high and low temperatures, showing that sub-Ohmic, high temperature environments lead to highly non-Markovian evolution, with cyclic backflows of Gaussian steerability from the environment to the system. Our results add to the understanding of the interplay between quantum correlations and non-Markovianity for CV systems, and could be implemented at the experimental level to quantify non-Markovianity in some physical scenarios.