Locality and universality of quantum memory effects

Liu, Bi-Heng; Wißmann, Steffen; Hu, Xiaomin; Zhang, C.; Huang, Yi; Li, C.-F.; Guo, Guang‐Can; Karlsson, Antti; Piilo, Jyrki; Breuer, Heinz‐Peter

doi:10.48550/arxiv.1403.4261

Cited by 3 publications

(4 citation statements)

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“…As in the case of geometric measures, the main drawback of the quantity N I H is the difficult optimization process, which makes this measure rather impractical. For the restricted case of [33] there has been some progress along this line [105,106], see also Section 5.1.1 and references therein.…”

Section: The Quantity N Imentioning

confidence: 99%

“…It has also been employed to analyze memory-kernel master equations [163,164], quantum semi-Markov process [11], classical noise [11,34,127,[165][166][167], in fermionic systems [168] and collisional models [169], and to study exciton-phonon dynamics in energy transfer of photosynthetic complexes [170,171]. Moreover this witness has been implemented experimentally within a linear optics set up [106,[172][173][174][175]. On the other hand, some connections have been found between the non-monotonic behavior of the trace distance and geometric phases [176], Loschmidt echo [177,178], dynamical recovering of the quantum coherence by applying local operations [179], and the appearance of system-environment correlations [180].…”

Section: Witnesses Based On Monotonicity Under Completely Positive Mapsmentioning

confidence: 99%

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Quantum non-Markovianity: characterization, quantification and detection

2014

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We present a comprehensive and up-to-date review of the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of a quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is provided. We then discuss several existing proposals to quantify the degree of non-Markovianity of quantum dynamics and to witness non-Markovian behavior, the latter providing sufficient conditions to detect deviations from strict Markovianity. Finally, we conclude by enumerating some timely open problems in the field and provide an outlook on possible research directions.

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Section: The Quantity N Imentioning

confidence: 99%

Section: Witnesses Based On Monotonicity Under Completely Positive Mapsmentioning

confidence: 99%

Quantum non-Markovianity: characterization, quantification and detection

2014

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“…The maximization involved in the definition of this measure can be greatly simplified since the optimal states must be orthogonal [21] and, even more, one can determine N by means of a local maximization over one state only [22]. This measure of non-Markovianity has been also investigated experimentally in all-optical settings [14,23,24].…”

Section: A Trace-distance Measurementioning

confidence: 99%

Quantum regression theorem and non-Markovianity of quantum dynamics

2014

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We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behaviour in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behaviour of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two points correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.Comment: 11 pages, 4 figure

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“…This provides an intuitive characterization of the presence of memory effects in terms of a temporary increase in the distinguishability of quantum states as a result of an information back-flow from the system and into the environment that is absent when the evolution is divisible [53]. As a result, a divisible evolution for which the single decay rate γ(t) ≥ 0 at all times will exhibit a monotonic decrease of the trace distance of any input state towards a (assumed to be unique) fixed point ρ f p of the Lindblad generator L [54]. On the contrary, as illustrated in Fig.…”

Section: The Modelmentioning

confidence: 99%

Efficiency of quantum controlled non-Markovian thermalization

et al. 2015

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We study optimal control strategies to optimize the relaxation rate towards the fixed point of a quantum system in the presence of a non-Markovian (NM) dissipative bath. Contrary to naive expectations that suggest that memory effects might be exploited to improve optimal control effectiveness, NM effects influence the optimal strategy in a non trivial way: we present a necessary condition to be satisfied so that the effectiveness of optimal control is enhanced by NM subject to suitable unitary controls. For illustration, we specialize our findings for the case of the dynamics of single qubit amplitude damping channels. The optimal control strategy presented here can be used to implement optimal cooling processes in quantum technologies and may have implications in quantum thermodynamics when assessing the efficiency of thermal micro-machines.

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Locality and universality of quantum memory effects

Cited by 3 publications

References 1 publication

Quantum non-Markovianity: characterization, quantification and detection

Quantum non-Markovianity: characterization, quantification and detection

Quantum regression theorem and non-Markovianity of quantum dynamics

Efficiency of quantum controlled non-Markovian thermalization

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