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arXiv:2109.09571 · Physical Review A

Quantum non-Markovian “casual bystander” environments

Adrián A. Budini

Published Dec 30, 2021• 4 citations
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Abstract

Quantum memory effects can be induced even when the (time-dependent) dynamical degrees of freedom associated to the environment are not affected at all by the open system during their joint coupled evolution. In this paper, based on a completely positive bipartite representation of the system-environment dynamics, we found the more general interactions that lead to this class of quantum non-Markovian ``casual bystander'' environments. General properties of the resulting dynamics are studied with a focus on the system-environment correlations, a collisional measurement-based representation, and the quantum regression hypothesis. Memory effects are also characterized through an operational approach, which in turn allows one to detect when the studied properties apply. Single and multipartite qubits dynamics support and exemplify the developed results.

DOI
10.1103/physreva.104.062216

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Quantum memory effects can be induced even when the (time-dependent) dynamical degrees of freedom associated to the environment are not affected at all by the open system during their joint coupled evolution. In this paper, based on a completely positive bipartite representation of the system-environment dynamics, we found the more general interactions that lead to this class of quantum non-Markovian ``casual bystander'' environments. General properties of the resulting dynamics are studied with a focus on the system-environment correlations, a collisional measurement-based representation, and the quantum regression hypothesis. Memory effects are also characterized through an operational approach, which in turn allows one to detect when the studied properties apply. Single and multipartite qubits dynamics support and exemplify the developed results.
The developing of (non-Markovian) memory effects strongly depends on the underlying system-environment dynamics. Here we study this problem in multipartite arrangements where all subsystems are coupled to each other by dephasing mechanisms that are taken into account through an underlying Markovian Lindblad dynamics characterized by a nondiagonal rate matrix. Taking as system and environment arbitrary sets of complementary subsystems, it is shown that both operational and nonoperational approaches to quantum non-Markovianity can be characterized in an exact analytical way. Similarly to previous studies about dissipative entanglement generation in this kind of dynamics [Seif, Wang, and Clerk, Phys. Rev. Lett. 128, 070402 (2022)], we found that memory effects can only emerge when a time-reversal symmetry is broken. Nevertheless, it is also found that departures from Markovianity can equivalently be represented through a statistical mixture of Markovian dephasing dynamics, which does not involve any system-environment entanglement. Specific bipartite and multipartite dynamics exemplify the main general results.
Quantum memory effects can be related to a bidirectional exchange of information between an open system and its environment, which in turn modifies the state and dynamical behavior of the last one. Nevertheless, non-Markovianity can also be induced by environments whose dynamics is not affected during the system evolution, implying the absence of any physical information exchange. An unsolved open problem in the formulation of quantum memory measures is the apparent impossibility of discerning between both paradigmatic cases. Here we present an operational scheme that, based on the outcomes of successive measurements processes performed over the system of interest, allows one to distinguish between both kinds of memory effects. The method accurately detects bidirectional information flows in diverse dissipative and dephasing non-Markovian open system 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 modeled 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 nonmonotonic time behavior of the heat flux serves as an indicator of non-Markovian behavior.
The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex structures are of central importance in many applications of quantum mechanics. The theoretical description, analysis and control of non-Markovian quantum processes play an important role in this context. While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects and represents the key property of non-Markovian quantum behavior. Here, we review recent ideas developing a general mathematical definition for non-Markoviantiy in the quantum regime and a measure for the degree of memory effects in the dynamics of open systems which are based on the exchange of information between system and environment. We further study the dynamical effects induced by the presence of system-environment correlations in the total initial state and design suitable methods to detect such correlations through local measurements on the open system.
Non-Markovian processes may arise in physics due to memory effects of environmental degrees of freedom. For quantum non-Markovianity, it is an ongoing debate to clarify whether such memory effects have a verifiable quantum origin, or whether they might equally be modeled by a classical memory. In this contribution, we propose a criterion to test locally for a truly quantum memory. The approach is agnostic with respect to the environment, as it solely depends on the local dynamics of the system of interest. Experimental realizations are particularly easy, as only single-time measurements on the system itself have to be performed. We study memory in a variety of physically motivated examples, both for a time-discrete case, and for time-continuous dynamics. For the latter, we are able to provide an interesting class of non-Markovian master equations with classical memory that allows for a physically measurable quantum trajectory representation.
We study a class of multipartite open quantum dynamics for systems with an arbitrary number of qubits. The non-Markovian quantum master equation can involve arbitrary single or multipartite and time-dependent dissipative coupling mechanisms, expressed in terms of strings of Pauli operators. We formulate the general constraints that guarantee the complete positivity of this dynamics. We characterize in detail the underlying mechanisms that lead to memory effects, together with properties of the dynamics encoded in the associated system rates. We specifically derive multipartite ``eternal'' non-Markovian master equations that we term hyperbolic and trigonometric due to the time dependence of their rates. For these models we identify a transition between positive and periodically divergent rates. We also study non-Markovian effects through an operational (measurement-based) memory witness approach.