Ancillary Gaussian modes activate the potential to witness non-Markovianity

TL;DR

This paper investigates how the number of modes affects the ability to detect non-Markovianity in continuous-variable quantum systems, revealing activation phenomena when multiple ancillary modes are used.

Contribution

It demonstrates that increasing the number of ancillary modes can activate the detection of non-Markovianity through correlation backflows, even in cases where single modes show no revivals.

Findings

Non-Markovian Gaussian evolutions can lack correlation revivals with one ancillary mode.

Adding two ancillary modes enables detection of correlation backflows.

Activation of non-Markovianity detection depends on the number of modes used.

Abstract

We study how the number of employed modes impacts the ability to witness non-Markovian evolutions via correlation backflows in continuous-variable quantum dynamics. We first prove the existence of non-Markovian Gaussian evolutions that do not show any revivals in the correlations between the mode evolving through the dynamics and a single ancillary mode. We then demonstrate how this scenario radically changes when two ancillary modes are considered. Indeed, we show that the same evolutions can show correlation backflows along a specific bipartition when three-mode states are employed, and where only one mode is subjected to the evolution. These results can be interpreted as a form of activation phenomenon in non-Markovianity detection and are proven for two types of correlations, entanglement and steering, and two classes of Gaussian evolutions, a classical noise model and the quantum Brownian motion model.