title: Non-Markovianity Hierarchy of Gaussian Processes and Quantum Amplification.
abstract: 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.
authors.affiliation: Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
authors.forename: Pietro
authors.initials: P
authors.lastname: Liuzzo-Scorpo
authors.affiliation: Department of Physics, University of Strathclyde, John Anderson Building, 107 Rottenrow, Glasgow G4 0NG, United Kingdom.
authors.forename: Wojciech
authors.initials: W
authors.lastname: Roga
authors.affiliation: Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.|Universidade Federal de Viçosa-Campus Florestal, LMG818 Km6, Minas Gerais, Florestal 35690-000, Brazil.
authors.forename: Leonardo A M
authors.initials: LA
authors.lastname: Souza
authors.affiliation: Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte, Caixa Postal 702, 30161-970, Brazil.
authors.forename: Nadja K
authors.initials: NK
authors.lastname: Bernardes
authors.affiliation: Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
authors.forename: Gerardo
authors.initials: G
authors.lastname: Adesso