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arXiv:2305.16136 · Physical Review A

Quantifying environment nonclassicality in dissipative open quantum dynamics

Adrián A. Budini

Published Oct 6, 2023• 4 citations
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Abstract

Open quantum systems are inherently coupled to their environments, which in turn also obey quantum dynamical rules. Restricting ourselves to dissipative dynamics, here we propose a measure that quantifies how far the action of an environment on a system departs from the influence of classical noise fluctuations. It is based on the lack of commutativity between the initial reservoir state and the total system-environment Hamiltonian. Independently of the nature of the dissipative system evolution, Markovian or non-Markovian, the measure can be written in terms of the dual propagator that defines the evolution of system operators. The physical meaning and properties of the proposed definition are discussed in detail and also characterized through different paradigmatic dissipative Markovian and non-Markovian open quantum dynamics.

DOI
10.1103/physreva.108.042203

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Open quantum systems are inherently coupled to their environments, which in turn also obey quantum dynamical rules. Restricting ourselves to dissipative dynamics, here we propose a measure that quantifies how far the action of an environment on a system departs from the influence of classical noise fluctuations. It is based on the lack of commutativity between the initial reservoir state and the total system-environment Hamiltonian. Independently of the nature of the dissipative system evolution, Markovian or non-Markovian, the measure can be written in terms of the dual propagator that defines the evolution of system operators. The physical meaning and properties of the proposed definition are discussed in detail and also characterized through different paradigmatic dissipative Markovian and non-Markovian open quantum dynamics.
The degree of non-Markovianity allows one to characterize quantum evolutions that depart from a Markovian regime in a similar way as the Schmidt number measures the degree of entanglement of pure states. Maximally non-Markovian dynamics are analogous to maximally entangled states [D. Chru\ifmmode \acute{s}\else \'{s}\fi{}ci\ifmmode \acute{n}\else \'{n}\fi{}ski and S. Maniscalco, Phys. Rev. Lett. 112, 120404 (2014)]. Here we demonstrate that there exists a class of maximally non-Markovian quantum evolutions where the associated environment (degrees of freedom not belonging to the system) obeys a Markovian (memoryless) dynamics, which in turn is unperturbed by the system state or dynamics. These properties imply the absence of any ``physical environment-to-system backflow of information.'' Non-Markovian features (as usual in quantum systems coupled to dissipative classical degrees of freedom) arise from a unidirectional dependence of the system dynamics on the reservoir states.
We study quantum non-Markovian dynamics of the Caldeira-Leggett model, a prototypical model for quantum Brownian motion describing a harmonic oscillator linearly coupled to a reservoir of harmonic oscillators. Employing the exact analytical solution of this model one can determine the size of memory effects for arbitrary couplings, temperatures, and frequency cutoffs. Here, quantum non-Markovianity is defined in terms of the flow of information between the open system and its environment, which is quantified through the Bures metric as distance measure for quantum states. This approach allows us to discuss quantum memory effects in the whole range from weak to strong dissipation for arbitrary Gaussian initial states. A comparison of our results with the corresponding results for the spin-boson problem show a remarkable similarity in the structure of non-Markovian behavior of the two paradigmatic models.
We characterize a class of superclassical non-Markovian open quantum system dynamics that are defined by their lack of measurement invasiveness when the corresponding observable commutates with the premeasurement state. This diagonal noninvasiveness guarantees that joint probabilities for measurement outcomes fulfill classical Kolmogorov consistency conditions. These features are fulfilled regardless of the previous (measurement) system history and are valid at arbitrary later times after an arbitrary system initialization. It is shown that a subclass of depolarizing dynamics, which are based on a (time-irreversible) nonunitary system-environment coupling, satisfy the required properties. The relationship with other operational [S. Milz et al., Phys. Rev. X 10, 041049 (2020)] and nonoperational [M. Banacki et al., Phys. Rev. A 107, 032202 (2023)] notions of classicality in non-Markovian open quantum systems is studied in detail and exemplified through different examples.
We investigate the correspondence between classical noise and quantum environments. Although it is known that classical noise can be mapped to quantum environments for pure dephasing and infinite-temperature dissipation processes, we show how finite-temperature dissipation can be also described using classical noise by introducing auxiliary systems and conservation. Taking a two-level system as an example, we construct the so-called central spin model with its couplings fluctuating with the classical noise and then acquire its statistical-average dynamics which captures the dissipation beyond infinite temperature. By adjusting the number of auxiliary systems and their initial states, the noise-based model reproduces both Markovian and non-Markovian evolution. We also find that different quantities of the two-level system are governed by different model parameters, indicating that the constructed model is an effective simulator for specific observables rather than an equivalent form of a realistic open system. In addition, the model is also applicable to investigate topical mechanisms of open systems, e.g., negative temperatures and asymmetric equidistant quenches.
In this PHD thesis, I address the study of the evolution of quantum correlations of continuous variable systems interacting with classical environments, portrayed by classical stochastic fields. In particular, the first goal is individuating the working regimes where a full quantum description of the system-environment interaction may be simulated with a stochastic approach. As a paradigmatic example, I consider quantum harmonic oscillators subject to phase diffusion and dissipation decoherence. My results show that the stochastic noise may take over the full quantum description of Markovian dephasing channels, while a stochastic approach to dissipation only works at a high temperature in the early stage of the dynamics. The second goal consists in better exploring the connection between the dynamics of correlations of the system, non-Markovianity and backflow of information. In many situations non-Markovianity cannot be proved but only revealed by means of appropriate witnesses, usually associated to backflow of information. My results show that stochastic phase diffusing and stochastic dissipative environments lead to non-Markovian dynamics, but their non-Markovianity stays unwitnessed unless revivals of correlations as nonclassicality, entanglement or discord are detected. This suggests that non-Markovianity sets the natural framework for revivals of correlations, but the true resource to obtain revivals is the backflow of information. The third goal consists in showing that effects of local or global noise on a bipartite system may easily be distinguished by means of standard laboratory techniques. Indeed, my results show that homodyne-detection-based schemes may discriminate the effects of a global stochastic noise affecting two probes from local perturbation, using as states of the probe ?lab-friendly? states.
One of the main goals of the theory of open quantum systems is to devise methods which help preserve the quantum properties of a system interacting with its environment.One possible pathway to achieve this goal is to use non-Markovian reservoirs, characterized by information backflows and revivals of certain quantum properties.These reservoirs usually require advanced engineering techniques, which may turn their implementation impractical.In this dissertation we propose an alternative technique: the injection of a classical colored noise, which induces the desired quantum non-Markovianity.In order to do that, we investigate the dynamics of a quantum system interacting with its surrounding environment and under the injection of a classical stochastic colored noise.A time-local master equation for the system is derived by using the stochastic wave function formalism and functional calculus.Afterwards, the non-Markovianity of the evolution is detected by using the Andersson, Cresser, Hall and Li measure, which is based on the decay rates of the master equation in canonical Lindblad-like form.Finally, we evaluate the measure for three different colored noises and study the interplay between environment and noise pump necessary to induce quantum non-Markovianity, as well as the energy balance of the system.