Information Backflow Research Articles

Non-Markovian dynamics of correlations: The composite effect of two channels and robust quantum correlation preserving by detuning

We investigate the influence of the composite effect and information backflow effect in non-Markovian channel on the dynamics of quantum correlation including quantum entanglement and quantum discord. It is found that, the composite effect of independent channels is not only harmful to the maintenance of quantum correlation but also unfavorable for the maintenance of classic correlation. In a non-Markovian channel, by regulating the discord between qubit and the center frequency of cavity model, the time of quantum correlation and classical correlation of the system can be effectively prolonged. Thus, the quantum information processing can be achieved more easily under larger detuning.

Non-Markovianity through flow of information between a system and an environment

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 new 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 [Phys. Rev. Lett. 112, 210402 (2014)] by Fanchini et al. 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.

Measuring non-Markovianity based on local quantum uncertainty

We introduce an alternative method based on local quantum uncertainty to measure non-Markovianity for an open quantum system. The local quantum uncertainty proposed by Girolami $et al$. [Phys. Rev. Lett. 110, 240402 (2013)] is defined by the minimum skew information from a local measurement perspective. The measure effectively captures the characteristics of non-Markovianity and has a clearly physical interpretation: in correlated bipartite systems, the non-Markovian (Markovian) process of a considered open subsystem corresponds to the increase (decrease) of quantum uncertainty of local observables of another measured free subsystem. Then the local quantum uncertainty is further discussed by carefully handling the square root of the density operator for the bipartite $2\ensuremath{\bigotimes}d$ systems. Specifically, for a two-qubit system we give an explicit expression of the local quantum uncertainty. Furthermore, by applying the measure to three typical non-Markovian noise channels, we find that the conditions of detecting the non-Markovianity are consistent with the results of existing measures for non-Markovianity, i.e., information backflow and divisibility.

Environmental correlations and Markovian to non-Markovian transitions in collisional models

We investigate the smallest set of requirements for inducing non-Markovian dynamics in a collisional model of open quantum systems. This is done by introducing correlations in the state of the environment and analyzing the divisibility of the quantum maps from consecutive time steps. Our model and results serve as a platform for the microscopic study of non-Markovian behavior as well as an example of a simple scenario of non-Markovianity with purely contractive maps, i.e. with no back-flow of information between system and environment.

Non-Markovianity of a quantum emitter in front of a mirror

We consider a quantum emitter ("atom") radiating in a one-dimensional (1D) photonic waveguide in the presence of a single mirror, resulting in a delay differential equation for the atomic amplitude. We carry out a systematic analysis of the non-Markovian (NM) character of the atomic dynamics in terms of refined, recently developed notions of quantum non-Markovianity such as indivisibility and information back-flow. NM effects are quantified as a function of the round-trip time and phase shift associated with the atom-mirror optical path. We find, in particular, that unless an atom-photon bound state is formed a finite time delay is always required in order for NM effects to be exhibited. This identifies a finite threshold in the parameter space, which separates the Markovian and non-Markovian regimes.

Monogamy and backflow of mutual information in non-Markovian thermal baths

We investigate the dynamics of information among the parties of tripartite systems. We start by proving two results concerning the monogamy of mutual information. The first one states that mutual information is monogamous for generic tripartite pure states. The second shows that, in general, mutual information is monogamous only if the amount of genuine tripartite correlations is large enough. Then, we analyze the internal dynamics of tripartite systems whose parties do not exchange energy. In particular, we allow for one of the subsystems to play the role of a finite thermal bath. As a result, we find a typical scenario in which local information tends to be converted into delocalized information. Moreover, we show that (i) the information flow is reversible for finite thermal baths at low temperatures, (ii) monogamy of mutual information is respected throughout the dynamics, and (iii) genuine tripartite correlations are typically present. Finally, we analytically calculate a quantity capable of revealing favorable regimes for non-Markovianity in our model.

Post-Markovian quantum master equations from classical environment fluctuations

In this paper we demonstrate that two commonly used phenomenological post-Markovian quantum master equations can be derived without using any perturbative approximation. A system coupled to an environment characterized by self-classical configurational fluctuations, the latter obeying a Markovian dynamics, defines the underlying physical model. Both Shabani-Lidar equation [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101(R) (2005)] and its associated approximated integrodifferential kernel master equation are obtained by tracing out two different bipartite Markovian Lindblad dynamics where the environment fluctuations are taken into account by an ancilla system. Furthermore, conditions under which the non-Markovian system dynamics can be unraveled in terms of an ensemble of measurement trajectories are found. In addition, a non-Markovian quantum jump approach is formulated. Contrary to recent analysis [L. Mazzola, E. M. Laine, H. P. Breuer, S. Maniscalco, and J. Piilo, Phys. Rev. A 81, 062120 (2010)], we also demonstrate that these master equations, even with exponential memory functions, may lead to non-Markovian effects such as an environment-to-system backflow of information if the Hamiltonian system does not commutate with the dissipative dynamics.

Non-Markovian dynamics and noise characteristics in continuous measurement of a solid-state charge qubit

We investigate the non-Markovian characteristics in continuous measurement of a charge qubit by a quantum point contact. The backflow of information from the reservoir to the system in the non-Markovian domain gives rise to strikingly different qubit relaxation and dephasing in comparison with the Markovian case. The intriguing non-Markovian dynamics is found to have a direct impact on the output noise feature of the detector. Unambiguously, we observe that the non-Markovian memory effect results in an enhancement of the signal-to-noise ratio, which can even exceed the upper limit of “4,” leading thus to the violation of the Korotkov-Averin bound in quantum measurement. Our study thus may open new possibilities to improve detector's measurement efficiency in a direct and transparent way.

Embedding non-Markovian quantum collisional models into bipartite Markovian dynamics

A wide class of non-Markovian completely positive master equations can be formulated on the basis of quantum collisional models. In this phenomenological approach the dynamics of an open quantum system is modeled through an ensemble of stochastic realizations that consist in the application at random times of a (collisional) completely positive transformation over the system state. In this paper, we demonstrate that these kinds of models can be embedded in bipartite Markovian Lindblad dynamics consisting of the system of interest and an auxiliary one. In contrast with phenomenological formulations, here the stochastic ensemble dynamics an the inter-event time interval statistics are obtained from a quantum measurement theory after assuming that the auxiliary system is continuously monitored in time. Models where the system inter-collisional dynamics is non-Markovian [B. Vacchini, Phys. Rev. A 87, 030101(R) (2013)] are also obtained from the present approach. The formalism is exemplified through bipartite dynamics that leads to non-Markovian system effects such as an environment-to-system back flow of information.

Non-Markovian qubit dynamics induced by Coulomb crystals

We investigate the back-flow of information in a system with a second-order structural phase transition, namely a quasi one-dimensional Coulomb crystal. Using standard Ramsey interferometry which couples a target ion (the system) to the rest of the chain (a phononic environment), we study the non-Markovian character of the resulting open system dynamics. We study two different time-scales and show that the back-flow of information pinpoints both the phase transition and different dynamical features of the chain as it approaches criticality. We also establish an exact link between the back-flow of information and the Ramsey fringe visibility.

Two-qubit non-Markovianity induced by a common environment

We study non-Markovianity as backflow of information in two-qubit systems. We consider a setting where, by changing the distance between the qubits, one can interpolate between independent reservoir and common reservoir scenarios. We demonstrate that non-Markovianity can be induced by the common reservoir and single out the physical origin of this phenomenon. We show that two-qubit non-Markovianity coincides with instances of non-divisibility of the corresponding dynamical map, and we discuss the pair of states maximizing information flowback. We also discuss the issue of additivity for the measure we use and in doing so, give an indication of its usefulness as a resource for multipartite quantum systems.

Non-Markovian Dynamics of an Open Two-Level System with Amplitude-Phase Damping

By use of the measure, the backflow of information presented recently, we study the non-Markovianity of the dynamics for a two-level system interacting with a zero-temperature structured environment via amplitude-phase coupling. In the limit of weak coupling between the system and its reservoir, the time-local non-Markovian master equation for the reduced state of the system is derived. Under the secular approximation, the exact analytic solution is obtained. Numerical simulations show that the amplitude and phase dampings can produce destructive interference to the backflow of information, leading to the weaker non-Markovianity of the compound dynamics compared with the dynamics of a single amplitude or phase damping model. We also study the characteristics of the initial-state pairs that maximize the backflow of information.

Non-Markovian dynamics for an open two-level system without rotating wave approximation: indivisibility versus backflow of information

By use of the two measures presented recently, the indivisibility and the backflow of information, we study the non-Markovianity of the dynamics for a two-level system interacting with a zero-temperature structured environment without using rotating wave approximation (RWA). In the limit of weak coupling between the system and the reservoir, and by expanding the time-convolutionless (TCL) generator to the forth order with respect to the coupling strength, the time-local non-Markovian master equation for the reduced state of the system is derived. Under the secular approximation, the exact analytic solution is obtained and the sufficient and necessary conditions for the indivisibility and the backflow of information for the system dynamics are presented. In the more general case, we investigate numerically the properties of the two measures for the case of Lorentzian reservoir. Our results show the importance of the counter-rotating terms to the short-time-scale non-Markovian behavior of the system dynamics, further expose the relations between the two measures and their rationality as non-Markovian measures. Finally, the complete positivity of the dynamics of the considered system is discussed.

On the relationship between non-Markovianity and entanglement protection

We test the conjecture that non-Markovian dynamics may help to protect quantum entanglement. To this end, we address an open system whose environment behaves either as a quantal system or as an effective reservoir, depending on the regime chosen to rule the system–environment dynamics. This allows us to study entanglement dynamics within Markovian and non-Markovian regimes. We focus on the recently introduced definition of quantum non-Markovianity that is based on the trace distance between pairs of initial states. The corresponding quantum measure for assessing the non-Markovianity of a quantum map Φ is submitted to test. We report cases for which signals non-Markovianity, even though Φ belongs to a purely dissipative regime. We argue that is not generally applicable to assess the non-Markovianity of a quantum process, because information is not always encoded in a way that depends on the distinguishability between states. When entanglement is used as the carrier of information, non-Markovianity should be diagnosed in terms of an entanglement measure. We thus compare the dynamics of Wooters concurrence and of trace distance between states, showing that they may behave qualitatively alike but leading to conflicting diagnosis about the backflow of information from the environment to the system. In contrast to other studies, in our case entanglement is transferred only to potential carriers of information, thereby excluding paradoxical situations that involve entangled reservoirs.

Quantifying non-Markovianity of continuous-variable Gaussian dynamical maps

We introduce a non-Markovianity measure for continuous-variable open quantum systems based on the idea put forward in H.-P. Breuer et al. [Phys. Rev. Lett. 103, 210401 (2009);], that is, by quantifying the flow of information from the environment back to the open system. Instead of the trace distance we use here the fidelity to assess distinguishability of quantum states. We employ our measure to evaluate non-Markovianity of two paradigmatic Gaussian channels: the purely damping channel and the quantum Brownian motion channel with Ohmic environment. We consider different classes of Gaussian states and look for pairs of states maximizing the backflow of information. For coherent states we find simple analytical solutions, whereas for squeezed states we provide both exact numerical and approximate analytical solutions in the weak coupling limit.

Measures of non-Markovianity: Divisibility versus backflow of information

We analyze two recently proposed measures of non-Markovianity: one based on the concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We provide a model to show that these two measures need not agree. In addition, we discuss possible generalizations and intricate relations between these measures.

Molecular-epigenetic aspects of phylo- and ontogenetic memory.

The problem of biological memory is discussed, and the theoretical unity of all types of memory-phylogenetic, immunological, and neuronal — is emphasized. This unity consists of the fact that the origin of anything “new” in living systems during phylo- or ontogenesis can be described within the framework of three principles: the “generator of variability of templates,” the “phenotypic expression of templates,” and the “effective selection of templates.” Here also lies the essence of the Darwinian approach to the problem of memory in general. The indicated three principles characterize the processes of transformation of feedback information in living nature both at the population level and at the level of individual living systems. They show how a backflow of information from the external environment to the organisms, leading to the formation of new adaptive responses in the course of ontogenesis, can be accomplished. Without contradicting the fundamentals of molecular biology and molecular genetics, they permit an explanation of the appearance of new adaptations, the accumulation of individual experience in ontogenesis, an unforeseen “inborn” genetic program.