Non-Markovianity hierarchy of Gaussian processes and quantum amplification

Liuzzo-Scorpo, Pietro and Roga, Wojciech and Souza, Leonardo A. M. and Bernardes, Nadja K. and Adesso, Gerardo (2017) Non-Markovianity hierarchy of Gaussian processes and quantum amplification. Physical Review Letters, 118 (5). pp. 1-6. 050401. ISSN 1079-7114 (

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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 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 temporary phase-insensitive amplification of Gaussian inputs beyond the fundamental quantum limit. Explicit examples and applications are discussed.