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:2003.12149 · Physical Review A

Dissipative generation of pure steady states and a gambler's ruin problem

Vladislav Popkov, Simon Essink, Corinna Kollath, Carlo Presilla A

Published Sep 8, 2020• 8 citations
arXivHTMLPDF

Abstract

We consider an open quantum system, with dissipation applied only to a part of its degrees of freedom, evolving via a quantum Markov dynamics. We demonstrate that, in the Zeno regime of large dissipation, the relaxation of the quantum system towards a pure quantum state is linked to the evolution of a classical Markov process towards a single absorbing state. The rates of the associated classical Markov process are determined by the original quantum dynamics. Extension of this correspondence to absorbing states with internal structure allows us to establish a general criterion for having a Zeno-limit nonequilibrium stationary state of arbitrary finite rank. An application of this criterion is illustrated in the case of an open $XXZ$ spin-1/2 chain dissipatively coupled at its edges to baths with fixed and different polarizations. For this system, we find exact nonequilibrium steady-state solutions of ranks 1 and 2.

DOI
10.1103/physreva.102.032205

Related papers

Obtaining pure steady states in nonequilibrium quantum systems with strong dissipative couplings

Vladislav Popkov, Carlo Presilla A

Dissipative preparation of a pure steady state usually involves a commutative action of a coherent and a dissipative dynamics on the target state. Namely, the target pure state is an eigenstate of both the coherent and dissipative parts of the dynamics. We show that working in the Zeno regime, i.e., for infinitely large dissipative coupling, one can generate a pure state by a noncommutative action, in the above sense, of the coherent and dissipative dynamics. A corresponding Zeno regime pureness criterion is derived. We illustrate the approach, looking at both its theoretical and applicative aspects, in the example case of an open $XXZ$ spin-$1/2$ chain, driven out of equilibrium by boundary reservoirs targeting different spin orientations. Using our criterion, we find two families of pure nonequilibrium steady states, in the Zeno regime, and calculate the dissipative strengths effectively needed to generate steady states which are almost indistinguishable from the target pure states.

arXiv:1509.04946•Physical Review A•Feb 16, 2016•32 citations

Effective quantum Zeno dynamics in dissipative quantum systems

Vladislav Popkov, Simon Essink, Carlo Presilla A +1 more

We investigate the time evolution of an open quantum system described by a Lindblad master equation with dissipation acting only on a part of the degrees of freedom ${\mathcal{H}}_{0}$ of the system, and targeting a unique dark state in ${\mathcal{H}}_{0}$. We show that, in the Zeno limit of large dissipation, the density matrix of the system traced over the dissipative subspace ${\mathcal{H}}_{0}$, evolves according to another Lindblad dynamics, with renormalized effective Hamiltonian and weak effective dissipation. This behavior is explicitly checked in the case of Heisenberg spin chains with one or both boundary spins strongly coupled to a magnetic reservoir. Moreover, the populations of the eigenstates of the renormalized effective Hamiltonian evolve in time according to a classical Markov dynamics. As a direct application of this result, we propose a computationally efficient exact method to evaluate the nonequilibrium steady state of a general system in the limit of strong dissipation.

arXiv:1806.10422•Physical Review A•Nov 7, 2018•39 citations

Targeting pure quantum states by strong noncommutative dissipation

Vladislav Popkov, Carlo Presilla A, Johannes Schmidt

We propose a solution to the problem of realizing a predefined and arbitrary pure quantum state, based on the simultaneous presence of coherent and dissipative dynamics, noncommuting on the target state and in the limit of strong dissipation. More precisely, we obtain a necessary and sufficient criterion whereby the nonequilibrium steady state (NESS) of an open quantum system described by a Lindblad master equation approaches a target pure state in the Zeno regime, i.e., for infinitely large dissipative coupling. We also provide an explicit formula for the characteristic dissipative strength beyond which the purity of the NESS becomes effective, thus paving the way to an experimental implementation of our criterion. For an illustration, we deal with targeting a Bell state, an arbitrary pure state of $N$ qubits, and a spin-helix state of $N$ qubits.

arXiv:1702.00287•Physical Review A•May 30, 2017•13 citations

Open quantum reaction-diffusion dynamics: Absorbing states and relaxation

Merlijn van Horssen, Juan P. Garrahan

We consider an extension of classical stochastic reaction-diffusion (RD) dynamics to open quantum systems. We study a class of models of hard-core particles on a one-dimensional lattice whose dynamics is generated by a quantum master operator. Particle hopping is coherent while reactions, such as pair annihilation or pair coalescence, are dissipative. These are quantum open generalizations of the A+A→⌀ and A+A→A classical RD models. We characterize the relaxation of the state towards the stationary regime via a decomposition of the system Hilbert space into transient and recurrent subspaces. We provide a complete classification of the structure of the recurrent subspace (and the nonequilibrium steady states) in terms of the dark states associated to the quantum master operator and its general spectral properties. We also show that, in one dimension, relaxation towards these absorbing dark states is slower than that predicted by a mean-field analysis due to fluctuation effects, in analogy with what occurs in classical RD systems. Numerical simulations of small systems suggest that the decay of the density in one dimension, in both the open quantum A+A→⌀ and A+A→A systems, behaves asymptotically as t-b with 1/2<b<1.

arXiv:1411.7913•Physical Review E•Mar 20, 2015•17 citations

Designing open quantum systems with known steady states: Davies generators and beyond

Jinkang Guo, Oliver Hart, Chi-Fang Chen +2 more

We provide a systematic framework for constructing generic models of nonequilibrium quantum dynamics with a target stationary (mixed) state. Our framework identifies (almost) all combinations of Hamiltonian and dissipative dynamics that relax to a steady state of interest, generalizing the Davies’ generator for dissipative relaxation at finite temperature to nonequilibrium dynamics targeting arbitrary stationary states. We focus on Gibbs states of stabilizer Hamiltonians, identifying local Lindbladians compatible therewith by constraining the rates of dissipative and unitary processes. Moreover, given terms in the Lindbladian not compatible with the target state, our formalism identifies the operations – including syndrome measurements and local feedback – one must apply to correct these errors. Our methods also reveal new models of quantum dynamics: for example, we provide a “measurement-induced phase transition” in which measurable two-point functions exhibit critical (power-law) scaling with distance at a critical ratio of the transverse field and rate of measurement and feedback. Time-reversal symmetry – defined naturally within our formalism – can be broken both in effectively classical and intrinsically quantum ways. Our framework provides a systematic starting point for exploring the landscape of dynamical universality classes in open quantum systems, as well as identifying new protocols for quantum error correction.

arXiv:2404.14538•Quantum•Jan 28, 2025•21 citations

Steady States of a Single Trapped-Ion Spin Coupled to an Engineered Non-Markovian Bath

Anthony Vogliano, Lewis Hahn, Fabien Lefebvre +5 more

Quantum simulation of open quantum systems offers a pathway towards better understanding various non-equilibrium physics that would otherwise be challenging to study. While most open quantum systems studied are modeled as being memory-less (obeying the Markov approximation), real baths generally are influenced by the system-bath interaction, and some systems existing in structured non-Markovian environments can display novel behavior as a result. Here we utilize a trapped ion quantum simulator to simulate a single spin-$1/2$ driven-dissipative system with a non-Markovian dissipation channel, and experimentally compare steady-states to those from an analogous Markovian bath. We observe that a non-Markovian dissipative channel can shift the steady-state even for a single qubit, to a regime inaccessible for Markovian dissipation. The techniques used here are compatible with many-body extensions of the model, which can not be simulated efficiently on a classical computer in general. Our work also opens up new possibilities in quantum reservoir engineering beyond the Markovian regime.

quant-pharXiv:2607.19286•Jul 22, 2026•0 citations
We consider an open quantum system, with dissipation applied only to a part of its degrees of freedom, evolving via a quantum Markov dynamics. We demonstrate that, in the Zeno regime of large dissipation, the relaxation of the quantum system towards a pure quantum state is linked to the evolution of a classical Markov process towards a single absorbing state. The rates of the associated classical Markov process are determined by the original quantum dynamics. Extension of this correspondence to absorbing states with internal structure allows us to establish a general criterion for having a Zeno-limit nonequilibrium stationary state of arbitrary finite rank. An application of this criterion is illustrated in the case of an open XXZXXZXXZ spin-1/2 chain dissipatively coupled at its edges to baths with fixed and different polarizations. For this system, we find exact nonequilibrium steady-state solutions of ranks 1 and 2.
Dissipative preparation of a pure steady state usually involves a commutative action of a coherent and a dissipative dynamics on the target state. Namely, the target pure state is an eigenstate of both the coherent and dissipative parts of the dynamics. We show that working in the Zeno regime, i.e., for infinitely large dissipative coupling, one can generate a pure state by a noncommutative action, in the above sense, of the coherent and dissipative dynamics. A corresponding Zeno regime pureness criterion is derived. We illustrate the approach, looking at both its theoretical and applicative aspects, in the example case of an open XXZXXZXXZ spin-1/21/21/2 chain, driven out of equilibrium by boundary reservoirs targeting different spin orientations. Using our criterion, we find two families of pure nonequilibrium steady states, in the Zeno regime, and calculate the dissipative strengths effectively needed to generate steady states which are almost indistinguishable from the target pure states.
We investigate the time evolution of an open quantum system described by a Lindblad master equation with dissipation acting only on a part of the degrees of freedom H0{\mathcal{H}}_{0}H0​ of the system, and targeting a unique dark state in H0{\mathcal{H}}_{0}H0​. We show that, in the Zeno limit of large dissipation, the density matrix of the system traced over the dissipative subspace H0{\mathcal{H}}_{0}H0​, evolves according to another Lindblad dynamics, with renormalized effective Hamiltonian and weak effective dissipation. This behavior is explicitly checked in the case of Heisenberg spin chains with one or both boundary spins strongly coupled to a magnetic reservoir. Moreover, the populations of the eigenstates of the renormalized effective Hamiltonian evolve in time according to a classical Markov dynamics. As a direct application of this result, we propose a computationally efficient exact method to evaluate the nonequilibrium steady state of a general system in the limit of strong dissipation.
We propose a solution to the problem of realizing a predefined and arbitrary pure quantum state, based on the simultaneous presence of coherent and dissipative dynamics, noncommuting on the target state and in the limit of strong dissipation. More precisely, we obtain a necessary and sufficient criterion whereby the nonequilibrium steady state (NESS) of an open quantum system described by a Lindblad master equation approaches a target pure state in the Zeno regime, i.e., for infinitely large dissipative coupling. We also provide an explicit formula for the characteristic dissipative strength beyond which the purity of the NESS becomes effective, thus paving the way to an experimental implementation of our criterion. For an illustration, we deal with targeting a Bell state, an arbitrary pure state of NNN qubits, and a spin-helix state of NNN qubits.
We consider an extension of classical stochastic reaction-diffusion (RD) dynamics to open quantum systems. We study a class of models of hard-core particles on a one-dimensional lattice whose dynamics is generated by a quantum master operator. Particle hopping is coherent while reactions, such as pair annihilation or pair coalescence, are dissipative. These are quantum open generalizations of the A+A→⌀ and A+A→A classical RD models. We characterize the relaxation of the state towards the stationary regime via a decomposition of the system Hilbert space into transient and recurrent subspaces. We provide a complete classification of the structure of the recurrent subspace (and the nonequilibrium steady states) in terms of the dark states associated to the quantum master operator and its general spectral properties. We also show that, in one dimension, relaxation towards these absorbing dark states is slower than that predicted by a mean-field analysis due to fluctuation effects, in analogy with what occurs in classical RD systems. Numerical simulations of small systems suggest that the decay of the density in one dimension, in both the open quantum A+A→⌀ and A+A→A systems, behaves asymptotically as t-b with 1/2<b<1.
We provide a systematic framework for constructing generic models of nonequilibrium quantum dynamics with a target stationary (mixed) state. Our framework identifies (almost) all combinations of Hamiltonian and dissipative dynamics that relax to a steady state of interest, generalizing the Davies’ generator for dissipative relaxation at finite temperature to nonequilibrium dynamics targeting arbitrary stationary states. We focus on Gibbs states of stabilizer Hamiltonians, identifying local Lindbladians compatible therewith by constraining the rates of dissipative and unitary processes. Moreover, given terms in the Lindbladian not compatible with the target state, our formalism identifies the operations – including syndrome measurements and local feedback – one must apply to correct these errors. Our methods also reveal new models of quantum dynamics: for example, we provide a “measurement-induced phase transition” in which measurable two-point functions exhibit critical (power-law) scaling with distance at a critical ratio of the transverse field and rate of measurement and feedback. Time-reversal symmetry – defined naturally within our formalism – can be broken both in effectively classical and intrinsically quantum ways. Our framework provides a systematic starting point for exploring the landscape of dynamical universality classes in open quantum systems, as well as identifying new protocols for quantum error correction.
Quantum simulation of open quantum systems offers a pathway towards better understanding various non-equilibrium physics that would otherwise be challenging to study. While most open quantum systems studied are modeled as being memory-less (obeying the Markov approximation), real baths generally are influenced by the system-bath interaction, and some systems existing in structured non-Markovian environments can display novel behavior as a result. Here we utilize a trapped ion quantum simulator to simulate a single spin-1/21/21/2 driven-dissipative system with a non-Markovian dissipation channel, and experimentally compare steady-states to those from an analogous Markovian bath. We observe that a non-Markovian dissipative channel can shift the steady-state even for a single qubit, to a regime inaccessible for Markovian dissipation. The techniques used here are compatible with many-body extensions of the model, which can not be simulated efficiently on a classical computer in general. Our work also opens up new possibilities in quantum reservoir engineering beyond the Markovian regime.