non-Markovian Conditions Research Articles

Fate of entanglement in magnetism under Lindbladian or non-Markovian dynamics and conditions for their transition to Landau-Lifshitz-Gilbert classical dynamics

Fate of entanglement in magnetism under Lindbladian or non-Markovian dynamics and conditions for their transition to Landau-Lifshitz-Gilbert classical dynamics

Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).

Limit behaviour of the minimal solution of a BSDE with singular terminal condition in the non Markovian setting

We use the functional Itô calculus to prove that the solution of a BSDE with singular terminal condition verifies at the terminal time: liminf _{tto T} Y(t) = xi = Y(T). Hence, we extend known results for a non-Markovian terminal condition.

Stochastic Schrödinger Equations and Conditional States: A General Non-Markovian Quantum Electron Transport Simulator for THz Electronics

A prominent tool to study the dynamics of open quantum systems is the reduced density matrix. Yet, approaching open quantum systems by means of state vectors has well known computational advantages. In this respect, the physical meaning of the so-called conditional states in Markovian and non-Markovian scenarios has been a topic of recent debate in the construction of stochastic Schrödinger equations. We shed light on this discussion by acknowledging the Bohmian conditional wavefunction (linked to the corresponding Bohmian trajectory) as the proper mathematical object to represent, in terms of state vectors, an arbitrary subset of degrees of freedom. As an example of the practical utility of these states, we present a time-dependent quantum Monte Carlo algorithm to describe electron transport in open quantum systems under general (Markovian or non-Markovian) conditions. By making the most of trajectory-based and wavefunction methods, the resulting simulation technique extends to the quantum regime, the computational capabilities that the Monte Carlo solution of the Boltzmann transport equation offers for semi-classical electron devices.

The freezing R\xe8nyi quantum discord

As a universal quantum character of quantum correlation, the freezing phenomenon is researched by geometry and quantum discord methods, respectively. In this paper, the properties of Rènyi discord is studied for two independent Dimer System coupled to two correlated Fermi-spin environments under the non-Markovian condition. We further demonstrate that the freezing behaviors still exist for Rènyi discord and study the effects of different parameters on this behaviors.

Positive entropy production rate induced by non-Markovianity

The non-Markovian effect on entropy production rate is an open question in quantum thermodynamics. By means of the change rate of the trace distance as the witness, we explore the non-Markovianities for their origin, i.e., from the initial correlation between the system and its heat reservoir and/or from the spectral density of the system-reservoir interaction. We show the possibility of positive entropy production rate regarding the initial correlation, which challenges the existing viewpoint of definitely negative entropy production rate under the non-Markovian condition. Our result is justified by an experimentally feasible model.

Non-Markovianity Measure Based on Brukner–Zeilinger Invariant Information for Unital Quantum Dynamical Maps**Supported by the National Natural Science Foundation of China under Grant No. 61505053, the Natural Science Foundation of Hunan Province under Grant No. 2015JJ3092, the Research Foundation of Education Bureau of Hunan Province, China under Grant No. 16B177, the School Foundation from the Hunan University of Arts and Science

A non-Markovianity measure based on Brukner–Zeilinger invariant information to characterize non-Markovian effect of open systems undergoing unital dynamical maps is proposed. The method takes advantage of non-increasing property of the Brukner–Zeilinger invariant information under completely positive and trace-preserving unital maps. The simplicity of computing the Brukner–Zeilinger invariant information is the advantage of the proposed measure because of mainly depending on the purity of quantum state. The measure effectively captures the characteristics of non-Markovianity of unital dynamical maps. As some concrete application, we consider two typical non-Markovian noise channels, i.e., the phase damping channel and the random unitary channel to show the sensitivity of the proposed measure. By investigation, we find that the conditions of detecting the non-Markovianity for the phase damping channel are consistent with the results of existing measures for non-Markovianity, i.e., information flow, divisibility and quantum mutual information. However, for the random unitary channel non-Markovian conditions are same to that of the information flow, but is different from that of the divisibility and quantum mutual information.

Quantum heat current under non-perturbative and non-Markovian conditions: Applications to heat machines.

We consider a quantum system strongly coupled to multiple heat baths at different temperatures. Quantum heat transport phenomena in this system are investigated using two definitions of the heat current: one in terms of the system energy and the other in terms of the bath energy. When we consider correlations among system-bath interactions (CASBIs)-which have a purely quantum mechanical origin-the definition in terms of the bath energy becomes different. We found that CASBIs are necessary to maintain the consistency of the heat current with thermodynamic laws in the case of strong system-bath coupling. However, within the context of the quantum master equation approach, both of these definitions are identical. Through a numerical investigation, we demonstrate this point for a non-equilibrium spin-boson model and a three-level heat engine model using the reduced hierarchal equations of motion approach under the strongly coupled and non-Markovian conditions. We observe the cyclic behavior of the heat currents and the work performed by the heat engine, and we find that their phases depend on the system-bath coupling strength. Through consideration of the bath heat current, we show that the efficiency of the heat engine decreases as the strength of the system-bath coupling increases, due to the CASBI contribution. In the case of a large system-bath coupling, the efficiency decreases further if the bath temperature is increased, even if the ratio of the bath temperatures is fixed, due to the discretized nature of energy eigenstates. This is also considered to be a unique feature of quantum heat engines.

Human and machine learning in non-Markovian decision making.

Humans can learn under a wide variety of feedback conditions. Reinforcement learning (RL), where a series of rewarded decisions must be made, is a particularly important type of learning. Computational and behavioral studies of RL have focused mainly on Markovian decision processes, where the next state depends on only the current state and action. Little is known about non-Markovian decision making, where the next state depends on more than the current state and action. Learning is non-Markovian, for example, when there is no unique mapping between actions and feedback. We have produced a model based on spiking neurons that can handle these non-Markovian conditions by performing policy gradient descent [1]. Here, we examine the model’s performance and compare it with human learning and a Bayes optimal reference, which provides an upper-bound on performance. We find that in all cases, our population of spiking neurons model well-describes human performance.

Non-Markovianity of open two-level system by means of quantum coherence

We propose an approach to measuring non-Markovianity of an open two-level system from quantum coherence perspective including l1 norm of coherence and quantum relative entropy of coherence, and derive corresponding non-Markovian conditions. Further, as a particular application, non-Markovian conditions of an open two-level system undergoing phase damping channel, random unitary channel and amplitude damping channel, respectively are investigated. Specifically speaking, for the three channels we obtain non-Markovian conditions based on l1 norm of coherence at any initial state of system, and find that non-Markovian conditions are the same as the conditions of other measurements, i.e., information back-flow, divisibility and quantum mutual entropy for the phase damping channel and amplitude damping channel, but non-Markovian conditions new and different from the conditions of other measurements for random unitary channel. On the other hand, for phase damping channel we obtain non-Markovian conditions based on quantum relative entropy of coherence at any initial state of system, which are the same as the conditions of other measures, i.e., information back-flow, divisibility and quantum mutual entropy. However, for the random unitary channel and amplitude damping channel we obtain non-Markovian conditions at maximally coherent state of system.

Quantum Discord Dynamics of Three Qubits in Non-Markovian Environments

We investigate the dynamics of pairwise quantum discord (QD) for a mixed three-qubit W-type state in three independent non-Markovian reservoirs at zero temperature, each of which is modeled by a leaky cavity with Lorentzian spectral density. The influence of the environment's amount of non-Markovianity, the detuning between the qubit frequency and the cavity centre frequency, and the purity of the initial state on the QD dynamics are analyzed in detail. It is found that in the non-Markovian regime the system-reservoir interactions induce QD revivals and oscillations no matter whether the detuning is zero or not. Moreover, QD can be preserved for a long time if the non-Markovian condition and the detuning condition are satisfied simultaneously.

Correlation dynamics of a two-qubit system in a Bell-diagonal state under non-identical local noises

The property of quantum correlation has been studied in recent years, especially for the quantum and classical correlations affected by environment. The dynamics of quantum and classical correlations in two-qubit system under identical local noise channels have been investigated recently. Here we will consider the dynamics of quantum and classical correlations when the local noise channels of two sides are not identical. We investigate the dynamics of quantum and classical correlations with three types of local noise channels in both Markovian and non-Markovian conditions, and show the decay rules of quantum and classical correlations with different types and parameter times of local noise channels.

Inverse engineering control in open quantum systems

We propose a scheme for inverse engineering control in open quantum systems. Starting from an undetermined time evolution operator, a time-dependent Hamiltonian is derived in order to guide the system to attain an arbitrary target state at a predefined time. We calculate the fidelity of our inverse engineering control protocol in the presence of the noise with respect to the stochastic fluctuation of the linear parameters of the Hamiltonian during the time evolution. For a special family of Hamiltonians for two-level systems, we show that the control evolution of the system under noise can be categorized into two standard decohering processes: dephasing and depolarization, for both Markovian and non-Markovian conditions. In particular, we illustrate our formalism by analyzing the robustness of the engineered target state against errors. Moreover, we discuss the generalization of the inverse protocol for higher-dimensional systems.

Non-Markovian effect on the precision of parameter estimation

We study the non-Markovian effect on the dynamics of the quantum Fisher information (QFI) by exactly solving a model consisting of a qubit system subjects to a zero-temperature reservoir for two different non-Markovian conditions: a high-$Q$ cavity slightly off-resonant with the qubit transition frequency and a nonperfect photonic band gap, respectively. The phenomenon that the QFI, namely, the precision of estimation, changes dramatically with the environment structure and is affected by the environment memory effects. We find that revivals and retardation of QFI loss may occur by adjusting the cavity-qubit detuning, in the first case, while partial QFI trapping occurs in nonideal photonic band gaps and the decreasing gap width seriously destroys coherence, thus reducing the precision of estimation. These features make the qubit system in non-Markovian environments a good candidate for implementation of quantum optics schemes and information with high precision.

Optimal control with monotonicity constraints for a parallel-server loss channel serving multi-class jobs

We study a parallel-server loss channel serving multi-class jobs, which appears in many real-world systems, e.g., cloud computing, multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM), and call centre. An -discounted optimal control with monotonicity constraints (OCMC) model over infinite time horizon is established by using the physical queueing model with linear revenue function. Existence of a solution to the OCMC model is proved, whose optimal value provides an upper bound of the corresponding values of the physical queueing model under Markovian decision rules. Algorithms with lower complexity in solving the OCMC model are proposed, which are further used to design an admission control policy for the loss channel. Furthermore, a simulation algorithm is proposed to implement the designed policy. Performance comparisons through numerical examples are conducted among our newly designed policy, the first-in first-out (FIFO) policy, an arbitrarily selected (AS) policy, and the Markov decision process (MDP) based threshold policy. Advantages and disadvantages of these policies are identified under different channel parameters and channel (e.g., Markovian and non-Markovian) conditions. Particularly, we find out that our designed policy outperforms the other three policies when the traffic intensity is relatively large, and the differences of the revenues per unit of time and the penalty costs among different classes of jobs are large.

Quantum Discord Dynamics in Two Different Non-Markovian Reservoirs

The quantum discord dynamics of two non-coupled two-level atoms independently interacting with their reservoir is studied under two kinds of non-Markovian conditions, namely, an off-resonant case with atomic transition frequency and a photonic band gap. In the first case, the phenomenon of the quantum discord loss and the oscillatory behavior of the quantum discord can occur by changing the detuning quantity and reducing the spectral coupling width for any initial Bell state. Under the second condition, the trapping phenomenon of the quantum discord can be presented by adjusting the width of gap, that is, the quantum discord of two atoms keep a nonzero constant for a long time.

Two-qubit entanglement dynamics for two different non-Markovian environments

We study the time behaviour of entanglement between two noninteracting qubits, each immersed in its own environment for two different non-Markovian conditions: a high-Q cavity slightly off-resonant with the qubit transition frequency and a nonperfect photonic band gap (PBG). We find that revivals and retardation of entanglement loss may occur by adjusting the cavity–qubit detuning, in the first case, while partial entanglement trapping occurs in a nonideal PBG.

Geometric measure of quantum discord in non-Markovian environments

We study the dynamics of geometric measure of quantum discord between two non-interacting qubits each immersed in its own non-Markovian environment with a spectal distribution representing the electromagnetic field inside off-resonant high-Q cavity. We compared the dynamics of geometric measure of quantum discord with quantum discord for an initial Werner-like state and conclude three important findings. First, when there is an instantaneous disappearance in the dynamics of quantum discord at some timepoints, there is a disappearance in geometric measure of quantum discord, but not instantly. Second, the sudden change in the decay rate of geometric measure of quantum discord might not imply the sudden change in the decay rate of the dynamics of quantum discord. Third, there is a preservation for a long time in both quantum discord and geometric measure of quantum discord when the detuning and non-Markovian conditions are simultaneously satisfied.

Heavy Traffic Analysis of a Controlled Multiclass Queueing Network via Weak Convergence Methods

The workload formulation due to Harrison and coworkers of multiclass queueing networks has been fundamental to its analysis. Until recently, there was no actual theory which started with the physical queue and showed that under heavy traffic conditions, the optimal costs could be approximated by those for an optimization problem using the ``limit'' workload equations. Recently, this was done via viscosity solution methods by Martins, Shreve, and Soner for one important class. For this same class of problems (and including the cases not treated there), we use weak convergence methods to show that the sequence of optimal costs for the original network converges to the optimal cost for the workload limit problem. The proof is simpler and allows weaker (and non-Markovian) conditions. It uses current techniques in weak convergence analysis. It seems to be the first analysis of such multiclass ``workload'' problems by weak convergence methods. The general structure of the development seems applicable to the analysis of more complex systems.

Mean first-passage time in the presence of colored noise: A random-telegraph-signal approach.

We derive an exact theory of the mean first-passage time for an arbitrary one-dimensional dynamical system driven by a multiplicative external noise with finite correlation time (colored noise). Three different cases of colored noise are discussed: the random telegraph signal, the pre-Gaussian noise, and the Ornstein-Uhlenbeck diffusion process. Using random telegraph signals as a tool, we fully solve the difficult problem of non-Markovian boundary conditions associated with such a problem. The analytic solution with these boundary conditions give a complete solution of the escape time in the presence of colored noise.