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:1607.07840 · Physical Review A

Determining stationary-state quantum properties directly from system-environment interactions

F. Nicacio, Mauro Paternostro, Alessandro Ferraro

Published Nov 28, 2016• 20 citations
arXivHTMLPDF

Abstract

Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between the Lyapunov equation for dynamical systems and the steady-state solutions of a time-independent Lindblad master equation for bosonic modes. Exploiting bona fide relations that characterize some genuine quantum properties (entanglement, classicality, and steerability), we obtain conditions on the dynamical parameters for which the system is driven to a steady state possessing such properties. We also develop a method to capture the symmetries of a steady state based on symmetries of the Lyapunov equation. All the results and examples can be useful for steady-state engineering processes.

DOI
10.1103/physreva.94.052129

Related papers

Symmetries and conserved quantities in Lindblad master equations

Victor V. Albert, Liang Jiang

This work is concerned with determination of the steady-state structure of time-independent Lindblad master equations, especially those possessing more than one steady state. The approach here is to treat Lindblad systems as generalizations of unitary quantum mechanics, extending the intuition of symmetries and conserved quantities to the dissipative case. We combine and apply various results to obtain an exhaustive characterization of the infinite-time behavior of Lindblad evolution, including both the structure of the infinite-time density matrix and its dependence on initial conditions. The effect of the environment in the infinite-time limit can therefore be tracked exactly for arbitrary state initialization and without knowledge of dynamics at intermediate time. As a consequence, sufficient criteria for determining the steady state of a Lindblad master equation are obtained. These criteria are knowledge of the initial state, a basis for the steady-state subspace, and all conserved quantities. We give examples of two-qubit dissipation and single-mode $d$-photon absorption where all quantities are determined analytically. Applications of these techniques to quantum information, computation, and feedback control are discussed.

arXiv:1310.1523•Physical Review A•Feb 21, 2014•446 citations

Stabilizing steady-state properties of open quantum systems with parameter engineering

Koray Aydoğan, Anthony W. Schlimgen, Kade Head-Marsden

Realistic quantum systems are affected by environmental loss, which is often seen as detrimental for applications in quantum technologies. Alternatively, weak coupling to an environment can aid in stabilizing highly entangled and mixed states, but determining optimal system-environment parameters can be challenging. Here, we describe a technique to optimize parameters for generating desired nonequilibrium steady states (NESSs) in driven-dissipative quantum systems governed by the Lindblad equation. We apply this approach to predict highly entangled and mixed NESSs in Ising, Kitaev, and Dicke models in several quantum phases.

arXiv:2503.09847•Physical Review Research•Apr 15, 2025•3 citations

ENTANGLEMENT IN OPEN QUANTUM SYSTEMS

Аурелиан Исар

In the framework of the theory of open systems based on quantum dynamical semigroups, we solve the master equation for two independent bosonic oscillators interacting with an environment in the asymptotic long-time regime. We give a description of the continuous-variable entanglement in terms of the covariance matrix of the quantum states of the considered system for an arbitrary Gaussian input state. Using the Peres-Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that the two non-interacting systems immersed in a common environment and evolving under a Markovian, completely positive dynamics become asymptotically entangled for certain environments, so that their non-local quantum correlations exist in the long-time regime.

•Jan 1, 2007•0 citations

Conditions for steady-state entanglement of quantum systems in a stationary environment under Markovian dissipation

Yuebing Zhou, Jiawei Hu, Hongwei Yu

We study the entanglement dynamics of an open quantum system composed of two identical two-level subsystems in a common stationary environment undergoing Markovian dissipation, with the help of a set of physical parameters defined with the collective transition coefficients of the system. We then systematically investigate the steady-state entanglement of such a system and obtain the necessary and sufficient condition for steady-state entanglement when it is initial-state dependent. We also show in particular conditions for steady-state entanglement in some circumstances and propose in general a conjecture for the necessary and sufficient condition when it is independent of the initial state.

Physical Review A•Mar 14, 2022•3 citations

Engineer coherent oscillatory modes in Markovian open quantum systems

Chun Hei Leung, Pak-Tik Fong, Tianyi Yan +1 more

We develop a novel framework to engineer persistent oscillatory modes in Markovian open quantum systems governed by a time-independent Lindblad master equation. We show that oscillatory modes can be created when the Hamiltonian and jump operator can be expressed in the same block-diagonal form. A key feature of the framework is that the dissipator of the Lindblad master equation are generally non-zero. We identify the weak and strong conditions, where the onset of the oscillatory modes is dependent and independent of the parameters of the system, respectively. Our method extends beyond the typical decoherence-free subspace approach, in which the dissipator is zero. We demonstrate the applicability of this framework using various models, showing how carefully tailored system-environment interactions can produce sustained coherent oscillations.

quant-pharXiv:2512.10144•Dec 12, 2025•0 citations

Lindblad Master Equations for Quantum Systems Coupled to Dissipative Bosonic Modes

Simon B. Jäger, Tom Schmit, Giovanna Morigi +2 more

We present a general approach to derive Lindblad master equations for a subsystem whose dynamics is coupled to dissipative bosonic modes. The derivation relies on a Schrieffer-Wolff transformation which allows us to eliminate the bosonic degrees of freedom after self-consistently determining their state as a function of the coupled quantum system. We apply this formalism to the dissipative Dicke model and derive a Lindblad master equation for the atomic spins, which includes the coherent and dissipative interactions mediated by the bosonic mode. This master equation accurately predicts the Dicke phase transition and gives the correct steady state. In addition, we compare the dynamics using exact diagonalization and numerical integration of the master equation with the predictions of semiclassical trajectories. We finally test the performance of our formalism by studying the relaxation of a NOON state and show that the dynamics captures quantum metastability.

arXiv:2203.03302•Physical Review Letters•Aug 2, 2022•60 citations
Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between the Lyapunov equation for dynamical systems and the steady-state solutions of a time-independent Lindblad master equation for bosonic modes. Exploiting bona fide relations that characterize some genuine quantum properties (entanglement, classicality, and steerability), we obtain conditions on the dynamical parameters for which the system is driven to a steady state possessing such properties. We also develop a method to capture the symmetries of a steady state based on symmetries of the Lyapunov equation. All the results and examples can be useful for steady-state engineering processes.
This work is concerned with determination of the steady-state structure of time-independent Lindblad master equations, especially those possessing more than one steady state. The approach here is to treat Lindblad systems as generalizations of unitary quantum mechanics, extending the intuition of symmetries and conserved quantities to the dissipative case. We combine and apply various results to obtain an exhaustive characterization of the infinite-time behavior of Lindblad evolution, including both the structure of the infinite-time density matrix and its dependence on initial conditions. The effect of the environment in the infinite-time limit can therefore be tracked exactly for arbitrary state initialization and without knowledge of dynamics at intermediate time. As a consequence, sufficient criteria for determining the steady state of a Lindblad master equation are obtained. These criteria are knowledge of the initial state, a basis for the steady-state subspace, and all conserved quantities. We give examples of two-qubit dissipation and single-mode ddd-photon absorption where all quantities are determined analytically. Applications of these techniques to quantum information, computation, and feedback control are discussed.
Realistic quantum systems are affected by environmental loss, which is often seen as detrimental for applications in quantum technologies. Alternatively, weak coupling to an environment can aid in stabilizing highly entangled and mixed states, but determining optimal system-environment parameters can be challenging. Here, we describe a technique to optimize parameters for generating desired nonequilibrium steady states (NESSs) in driven-dissipative quantum systems governed by the Lindblad equation. We apply this approach to predict highly entangled and mixed NESSs in Ising, Kitaev, and Dicke models in several quantum phases.
In the framework of the theory of open systems based on quantum dynamical semigroups, we solve the master equation for two independent bosonic oscillators interacting with an environment in the asymptotic long-time regime. We give a description of the continuous-variable entanglement in terms of the covariance matrix of the quantum states of the considered system for an arbitrary Gaussian input state. Using the Peres-Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that the two non-interacting systems immersed in a common environment and evolving under a Markovian, completely positive dynamics become asymptotically entangled for certain environments, so that their non-local quantum correlations exist in the long-time regime.
We study the entanglement dynamics of an open quantum system composed of two identical two-level subsystems in a common stationary environment undergoing Markovian dissipation, with the help of a set of physical parameters defined with the collective transition coefficients of the system. We then systematically investigate the steady-state entanglement of such a system and obtain the necessary and sufficient condition for steady-state entanglement when it is initial-state dependent. We also show in particular conditions for steady-state entanglement in some circumstances and propose in general a conjecture for the necessary and sufficient condition when it is independent of the initial state.
We develop a novel framework to engineer persistent oscillatory modes in Markovian open quantum systems governed by a time-independent Lindblad master equation. We show that oscillatory modes can be created when the Hamiltonian and jump operator can be expressed in the same block-diagonal form. A key feature of the framework is that the dissipator of the Lindblad master equation are generally non-zero. We identify the weak and strong conditions, where the onset of the oscillatory modes is dependent and independent of the parameters of the system, respectively. Our method extends beyond the typical decoherence-free subspace approach, in which the dissipator is zero. We demonstrate the applicability of this framework using various models, showing how carefully tailored system-environment interactions can produce sustained coherent oscillations.
We present a general approach to derive Lindblad master equations for a subsystem whose dynamics is coupled to dissipative bosonic modes. The derivation relies on a Schrieffer-Wolff transformation which allows us to eliminate the bosonic degrees of freedom after self-consistently determining their state as a function of the coupled quantum system. We apply this formalism to the dissipative Dicke model and derive a Lindblad master equation for the atomic spins, which includes the coherent and dissipative interactions mediated by the bosonic mode. This master equation accurately predicts the Dicke phase transition and gives the correct steady state. In addition, we compare the dynamics using exact diagonalization and numerical integration of the master equation with the predictions of semiclassical trajectories. We finally test the performance of our formalism by studying the relaxation of a NOON state and show that the dynamics captures quantum metastability.