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arXiv:2101.10308 · Physical Review A

Detection of bidirectional system-environment information exchanges

Adrián A. Budini

Published Jan 22, 2021• 9 citations
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Abstract

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.

DOI
10.1103/physreva.103.012221

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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.
The exchange of information between an open quantum system and its environment allows us to discriminate among different kinds of dynamics, in particular detecting memory effects to characterize non-Markovianity. Here, we investigate the role played by the system-environment correlations and the environmental evolution in the flow of information. First, we derive general conditions ensuring that two generalized dephasing microscopic models of the global system-environment evolution result exactly in the same open-system dynamics, for any initial state of the system. Then, we use the trace distance to quantify the distinct contributions to the information inside and outside the open system in the two models. Our analysis clarifies how the interplay between system-environment correlations and environmental-state distinguishability can lead to the same information flow from and toward the open system, despite significant qualitative and quantitative differences at the level of the global evolution.
Quantum memory effects can be qualitatively understood as a consequence of an environment-to-system backflow of information. Here, we analyze and compare how this concept is interpreted and implemented in different approaches to quantum non-Markovianity. We study a nonoperational approach, defined by the distinguishability between two system states characterized by different initial conditions, and an operational approach, which is defined by the correlation between different outcomes associated to successive measurement processes performed over the system of interest. The differences, limitations, and vantages of each approach are characterized in detail by considering diverse system-environment models and dynamics. As a specific example, we study a non-Markovian depolarizing map induced by the interaction of the system of interest with an environment characterized by incoherent and coherent self-dynamics.
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.
Mixing dynamical maps describing open quantum systems can lead from Markovian to non-Markovian processes. Being surprising and counter-intuitive, this result has been used as argument against characterization of non-Markovianity in terms of information exchange. Here, we demonstrate that, quite the contrary, mixing can be understood in a natural way which is fully consistent with existing theories of memory effects. In particular, we show how mixing-induced non-Markovianity can be interpreted in terms of the distinguishability of quantum states, system-environment correlations and the information flow between system and environment.
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.
Exchange of information between a quantum system and its surrounding environment plays a fundamental role in the study of the dynamics of open quantum systems. Here we discuss the role of the information exchange in the non-Markovian behavior of dynamical quantum processes following the decoherence approach, where we consider a quantum system that is initially correlated with its measurement apparatus, which in turn interacts with the environment. We introduce a way of looking at the information exchange between the system and environment using the quantum loss, which is shown to be closely related to the measure of non-Markovianity based on the quantum mutual information. We also extend the results of Fanchini et al. [Phys. Rev. Lett. 112, 210402 (2014)] in several directions, providing a more detailed investigation of the use of the accessible information for quantifying the backflow of information from the environment to the system. Moreover, we reveal a clear conceptual relation between the entanglement- and mutual-information-based measures of non-Markovianity in terms of the quantum loss and accessible information. We compare different ways of studying the information flow in two theoretical examples. We also present experimental results on the investigation of the quantum loss and accessible information for a two-level system undergoing a zero temperature amplitude damping process. We use an optical approach that allows full access to the state of the environment.