Non-Markovianity Hierarchy of Gaussian Processes and Quantum Amplification

TL;DR

This paper develops a hierarchy to classify Gaussian process dynamics in continuous variable quantum systems, distinguishing Markovian and non-Markovian behaviors, and links weak non-Markovianity to temporary quantum amplification beyond fundamental limits.

Contribution

It introduces a hierarchy of Gaussian process evolutions, provides criteria for classification, and reveals operational significance of weak non-Markovianity in quantum amplification.

Findings

Classified Gaussian channels by non-Markovianity degree

Established criteria based on Gaussian map positivity

Linked weak non-Markovianity to temporary quantum amplification

Abstract

We investigate dynamics of Gaussian states of continuous variable systems under Gaussianity preserving channels. We introduce a hierarchy of such evolutions encompassing Markovian, 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 classify all single-mode phase-insensitive Gaussian channels according to their non-Markovianity degree, and show that weak non-Markovianity has an operational significance as it leads to temporary amplification of Gaussian inputs beyond the fundamental quantum limit. Explicit examples and applications are discussed.