Non-Markovianity hierarchy of Gaussian processes and quantum amplification - Liuzzo-Scorpo, Pietro; Roga, Wojciech; Souza, Leonardo A.M.; Bernardes, Nadja K.; Adesso, Gerardo (American Physical Society, 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.