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Register a new userA classical appraisal of quantum definitions of non-Markovian dynamics
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Authors
Bassano Vacchini
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We consider the issue of non-Markovianity of a quantum dynamics starting from a comparison with the classical definition of Markovian process. We point to the fact that two sufficient but not necessary signatures of non-Markovianity of a classical process find their natural quantum counterpart in recently introduced measures of quantum non-Markovianity. This behavior is analyzed in detail for quantum dynamics which can be built taking as input a class of classical processes.
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We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular, we remark on the deep relation of the short time non-Markovian behavior with the revivals of the average fidelity amplitude-a fundamental quantity used to measure sensitivity to perturbations and to identify quantum chaos. The long time behavior is established as a finite size effect which vanishes for large enough environments.
The non-Markovian nature of quantum systems recently turned to be a key subject for investigations on open quantum system dynamics. Many studies, from its theoretical grounding to its usefulness as a resource for quantum information processing and experimental demonstrations, have been reported in the literature. Typically, in these studies, a structured reservoir is required to make non-Markovian dynamics to emerge. Here, we investigate the dynamics of a qubit interacting with a bosonic bath and under the injection of a classical stochastic colored noise. A canonical Lindblad-like master equation for the system is derived, using the stochastic wavefunction formalism. Then, the non-Markovianity of the evolution is witnessed using the Andersson, Cresser, Hall and Li measure. We evaluate the measure for three different noises and study the interplay between environment and noise pump necessary to generate quantum non-Markovianity, as well as the energy balance of the system. Finally, we discuss the possibility to experimentally implement the proposed model.
We provide an experimental study of the relationship between the action of different classical noises on the dephasing dynamics of a two-level system and the non-Markovianity of the quantum dynamics. The two-level system is encoded in the photonic polarization degrees of freedom and the action of the noise is obtained via a spatial light modulator, thus allowing for an easy engineering of different random environments. The quantum non-Markovianity of the dynamics driven by classical Markovian and non-Markovian noise, both Gaussian and non-Gaussian, is studied by means of the trace distance. Our study clearly shows the different nature of the notion of non-Markovian classical process and non-Markovian quantum dynamics.
We study the dynamics of a quantum system whose interaction with an environment is described by a collision model, i.e. the open dynamics is modelled through sequences of unitary interactions between the system and the individual constituents of the environment, termed ancillas, which are subsequently traced out. In this setting non-Markovianity is introduced by allowing for additional unitary interactions between the ancillas. For this model, we identify the relevant system-environment correlations that lead to a non-Markovian evolution. Through an equivalent picture of the open dynamics, we introduce the notion of memory depth where these correlations are established between the system and a suitably sized memory rendering the overall system+memory evolution Markovian. We extend our analysis to show that while most system-environment correlations are irrelevant for the dynamical characterization of the process, they generally play an important role in the thermodynamic description. Finally, we show that under an energy-preserving system-environment interaction, a non-monotonic time behaviour of the heat flux serves as an indicator of non-Markovian behaviour.
Quantum speed limit (QSL) under noise has drawn considerable attention in real quantum computational processes and quantum communication. Though non-Markovian noise is proven to be able to accelerate quantum evolution for a damped Jaynes-Cummings model, in this work we show that non-Markovianity may even slow down the quantum evolution of an experimentally controllable photon system. As an important application, QSL time of a photon can be well controlled by regulating the relevant environment parameter properly, which is close to reach the currently available photonic experimental technology.
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