Non-Markovianity Hierarchy of Gaussian Processes and Quantum Amplification
Pietro Liuzzo-Scorpo, Wojciech Roga, Leonardo A. M. Souza, Nadja K. Bernardes, Gerardo Adesso · Physical Review Letters · 2017
We investigate the dynamics of Gaussian states of continuous variable systems under Gaussianity-preserving channels. We introduce a hierarchy of such evolutions encompassing Markovian and 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 present an intuitive classification of all one-mode Gaussian channels according to their non-Markovianity degree and show that weak non-Markovianity has an operational significance, as it leads to a temporary phase-insensitive amplification of Gaussian inputs beyond the fundamental quantum limit. Explicit examples and applications are discussed.