Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1312.0396 · Physical Review A

Quantification and control of non-Markovian evolution in finite quantum systems via feedback

Nicholas Chancellor, C. Petri, Lorenzo Campos Venuti, Anthony F. J. Levi, Stephan Haas

Published May 19, 2014• 4 citations
arXivHTMLPDF

Abstract

We consider the unitary time evolution of continuous quantum-mechanical systems confined to a cavity in contact with a finite bath of variable size. We define a measure relating to (non-)Markovianity which parallels the standard one for the case of integrable Lindbladian dynamics but has the advantage of being numerically tractable also for large many-particle systems. The relevant time scales are identified which characterize non-Markovian transient behavior, boundary-scattering-induced non-Markovian oscillations at intermediate times, and non-Markovian rephasing events at long time scales. It is shown how these time scales can be controlled by tunable parameters such as the bath size and the strength of the system-bath coupling.

DOI
10.1103/physreva.89.052119

Related papers

Control of Pseudo-Markovian Evolution in Finite Quantum Systems via Feedback

Nicholas Chancellor, C. Petri, Lorenzo Campos Venuti +2 more

We consider the unitary time evolution of continuous quantum mechanical systems confined to a cavity in contact with a finite bath of variable size. Measures for Markovianity for such finite system-bath configurations are developed in terms of Hilbert-Schmidt distances of time evolving wave packets. The relevant time scales are identified, which characterize pseudo-Markovian transient behavior, boundary scattering induced non-Markovian oscillations at intermediate times, and non-Markovian rephasing events at long time scales. It is shown how these time scales can be controlled by tunable parameters such as the bath size and the strength of the system-bath coupling.

•Dec 2, 2013•0 citations

Non-Markovian quantum dynamics and classical chaos

Ignacio García-Mata, Carlos Pineda, Diego A. Wisniacki

We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular, we remark on the deep relation of the short time non-Markovian behavior with the revivals of the average fidelity amplitude---a fundamental quantity used to measure sensitivity to perturbations and to identify quantum chaos. The long time behavior is established as a finite size effect which vanishes for large enough environments.

arXiv:1204.3614•Physical Review A•Aug 20, 2012•17 citations

Completely-positive non-signalling non-Markovian dynamics

Serhii Kryhin, Vivishek Sudhir

We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting continuous-time dynamics is an integro-differential equation that augments the Gorini-Kossakowski-Sudarshan-Lindblad equation with a memory integral, and is capable of describing the quantum state of systems exposed to noise with any integrable power spectral density with no further approximations. We then establish a formalism to evaluate multi-time correlations of measurement outcomes in this general setting, obviating the need for a regression theorem. As an application, we derive the emission spectrum of a driven two-level system coupled to a non-Markovian bath: the familiar Mollow triplet acquires a frequency-dependent linewidth that encodes the memory of the bath. Our work provides a rigorous yet transparent description of the quantum state of non-Markovian systems, opening the door for state estimation and state-based quantum control beyond the Markovian regime.

quant-pharXiv:2605.03197•May 6, 2026•0 citations

Abrupt transitions between Markovian and non-Markovian dynamics in open quantum systems

Shengshi Pang, Todd A. Brun, Andrew N. Jordan

A rapid restoration of the bath state is usually required to induce Markovian dynamics for an open quantum system, which typically can be realized only in limits such as weak system-bath coupling and infinitely large bath. In this work, we investigate the Markovianity of a qubit system coupled to a single-qubit bath with the qubit bath being continuously refreshed by quantum cooling. A surprising result is that there exists a finite threshold for the cooling rate at which the system transitions from non-Markovian dynamics to Markovian dynamics, which is in sharp contrast to the usual understanding that Markovian dynamics is an asymptotic behavior under the Born-Markov approximation. We also study the time correlation of the bath, and find that the decay rate of bath time correlation is of the same order as the system evolution speed. This suggests that quantum Markovian dynamics can exist beyond the usual short bath correlation limit.

arXiv:1712.10109•Dec 29, 2017•3 citations

Effects of non-Markovian squeezed bath on the dynamics of open systems

Arapat Ablimit, Feng-Hua Ren, Run-Hong He +2 more

Control of the dynamics of an open quantum system is crucial in quantum information processing. Basically there are two ways: one is the control on the system and the other is tuning the bath parameters. In this paper, we use the latter to analyze the non-Markovian dynamics of the open system. The model is that the system is immersed in non-Markovian squeezed baths. For the dynamics, a non-Markovian master eqation is obtained using the quantum state diffusion (QSD) equation technique for the weak system-bath couplings. We use the adiabatic evolution or quantum state transmission as examples to analyze the effects of the bath parameters: non-Markovianity $γ$, the squeezed direction $θ$ and squeezed strength $r$. For the adiabatic or state transmission fidelity, the calculation results show that they both can be enhanced by a smaller $γ$ or bigger $p$-quadrature. Interestingly, when $0<θ<π/2$, the squeezed quadrature is determined by the combination of $r$ and $θ$, and by numerical simulation we find that the fidelity peak occurs at $r=1-2θ/π$. The fidelities increase with increasing $r$ when $r\in (0,1-2θ/π]$. When $θ\geπ/2$, lower fidelities are obtained due to the squeezed bath. Our results show that the dynamics of the open systems can be effectively controlled by reservoir enginerring.

arXiv:2304.04223•Apr 9, 2023•1 citation

Markovian Embeddings of Non-Markovian Quantum Systems: Coupled Stochastic and Quantum Master Equations for Non-Markovian Quantum Systems

Hendra I. Nurdin

Quantum Markov models are employed ubiqui-tously in quantum physics and in quantum information theory due to their relative simplicity and analytical tractability. In particular, these models are known to give accurate approxi-mations for a wide range of quantum optical and meso scopic systems. However, in general, the validity of the Markov approximation entails assumptions regarding properties of the system of interest and its environment, which may not be satisfied or accurate in arbitrary physical systems. Therefore, developing useful modelling tools for general non-Markovian quantum systems for which the Markov approximation is inappropriate or deficient is an undertaking of significant importance. This work considers non-Markovian principal quantum systems that can be embedded in a larger Markovian quantum system with one or more compound baths consisting of an auxiliary quantum system and a quantum white noise field, and derives a set of coupled stochastic and quantum master equations for embedded non-Markovian quantum systems. The case of a purely Hamiltonian coupling between the principal and auxiliary systems as a closed system without coupling to white noises is included as a special case. The results are expected to be of interest for (open-loop and feedback) control of continuous-time non-Markovian systems and studying reduced models for numerical simulation of such systems. They may also shed more light on the general structure of continuous-time non-Markovian quantum systems.

arXiv:2312.00134•IEEE Conference on Decision and Control (CDC)•Dec 13, 2023•1 citation
We consider the unitary time evolution of continuous quantum-mechanical systems confined to a cavity in contact with a finite bath of variable size. We define a measure relating to (non-)Markovianity which parallels the standard one for the case of integrable Lindbladian dynamics but has the advantage of being numerically tractable also for large many-particle systems. The relevant time scales are identified which characterize non-Markovian transient behavior, boundary-scattering-induced non-Markovian oscillations at intermediate times, and non-Markovian rephasing events at long time scales. It is shown how these time scales can be controlled by tunable parameters such as the bath size and the strength of the system-bath coupling.
We consider the unitary time evolution of continuous quantum mechanical systems confined to a cavity in contact with a finite bath of variable size. Measures for Markovianity for such finite system-bath configurations are developed in terms of Hilbert-Schmidt distances of time evolving wave packets. The relevant time scales are identified, which characterize pseudo-Markovian transient behavior, boundary scattering induced non-Markovian oscillations at intermediate times, and non-Markovian rephasing events at long time scales. It is shown how these time scales can be controlled by tunable parameters such as the bath size and the strength of the system-bath coupling.
We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular, we remark on the deep relation of the short time non-Markovian behavior with the revivals of the average fidelity amplitude---a fundamental quantity used to measure sensitivity to perturbations and to identify quantum chaos. The long time behavior is established as a finite size effect which vanishes for large enough environments.
We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting continuous-time dynamics is an integro-differential equation that augments the Gorini-Kossakowski-Sudarshan-Lindblad equation with a memory integral, and is capable of describing the quantum state of systems exposed to noise with any integrable power spectral density with no further approximations. We then establish a formalism to evaluate multi-time correlations of measurement outcomes in this general setting, obviating the need for a regression theorem. As an application, we derive the emission spectrum of a driven two-level system coupled to a non-Markovian bath: the familiar Mollow triplet acquires a frequency-dependent linewidth that encodes the memory of the bath. Our work provides a rigorous yet transparent description of the quantum state of non-Markovian systems, opening the door for state estimation and state-based quantum control beyond the Markovian regime.
A rapid restoration of the bath state is usually required to induce Markovian dynamics for an open quantum system, which typically can be realized only in limits such as weak system-bath coupling and infinitely large bath. In this work, we investigate the Markovianity of a qubit system coupled to a single-qubit bath with the qubit bath being continuously refreshed by quantum cooling. A surprising result is that there exists a finite threshold for the cooling rate at which the system transitions from non-Markovian dynamics to Markovian dynamics, which is in sharp contrast to the usual understanding that Markovian dynamics is an asymptotic behavior under the Born-Markov approximation. We also study the time correlation of the bath, and find that the decay rate of bath time correlation is of the same order as the system evolution speed. This suggests that quantum Markovian dynamics can exist beyond the usual short bath correlation limit.
Control of the dynamics of an open quantum system is crucial in quantum information processing. Basically there are two ways: one is the control on the system and the other is tuning the bath parameters. In this paper, we use the latter to analyze the non-Markovian dynamics of the open system. The model is that the system is immersed in non-Markovian squeezed baths. For the dynamics, a non-Markovian master eqation is obtained using the quantum state diffusion (QSD) equation technique for the weak system-bath couplings. We use the adiabatic evolution or quantum state transmission as examples to analyze the effects of the bath parameters: non-Markovianity γγγ, the squeezed direction θθθ and squeezed strength rrr. For the adiabatic or state transmission fidelity, the calculation results show that they both can be enhanced by a smaller γγγ or bigger ppp-quadrature. Interestingly, when 0<θ<π/20<θ<π/20<θ<π/2, the squeezed quadrature is determined by the combination of rrr and θθθ, and by numerical simulation we find that the fidelity peak occurs at r=1−2θ/πr=1-2θ/πr=1−2θ/π. The fidelities increase with increasing rrr when r∈(0,1−2θ/π]r\in (0,1-2θ/π]r∈(0,1−2θ/π]. When θ≥π/2θ\geπ/2θ≥π/2, lower fidelities are obtained due to the squeezed bath. Our results show that the dynamics of the open systems can be effectively controlled by reservoir enginerring.
Quantum Markov models are employed ubiqui-tously in quantum physics and in quantum information theory due to their relative simplicity and analytical tractability. In particular, these models are known to give accurate approxi-mations for a wide range of quantum optical and meso scopic systems. However, in general, the validity of the Markov approximation entails assumptions regarding properties of the system of interest and its environment, which may not be satisfied or accurate in arbitrary physical systems. Therefore, developing useful modelling tools for general non-Markovian quantum systems for which the Markov approximation is inappropriate or deficient is an undertaking of significant importance. This work considers non-Markovian principal quantum systems that can be embedded in a larger Markovian quantum system with one or more compound baths consisting of an auxiliary quantum system and a quantum white noise field, and derives a set of coupled stochastic and quantum master equations for embedded non-Markovian quantum systems. The case of a purely Hamiltonian coupling between the principal and auxiliary systems as a closed system without coupling to white noises is included as a special case. The results are expected to be of interest for (open-loop and feedback) control of continuous-time non-Markovian systems and studying reduced models for numerical simulation of such systems. They may also shed more light on the general structure of continuous-time non-Markovian quantum systems.