Number of steady states of quantum evolutions
arXiv:2404.00440 · doi:10.1038/s41598-024-64040-5
Abstract
We prove sharp universal upper bounds on the number of steady and asymptotic states of discrete- and continuous-time Markovian evolutions of open quantum systems. We show that the bounds depend only on the dimension of the system and not on the details of the dynamics. A comparison with similar bounds deriving from a recent spectral conjecture for Markovian evolutions is also provided.
arXiv comment16 pages, 1 figure
References in corpus (29)
- Decoherence Free Subspaces for Quantum Computation
- Noiseless Quantum Codes
- Symmetries and conserved quantities in Lindblad master equations
- Spectral theory of Liouvillians for dissipative phase transitions
- Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
- Critical dynamical properties of a first-order dissipative phase transition
- Quantum memories based on engineered dissipation
- Analysis of quantum semigroups with GKS--Lindblad generators II. General
- Universal spectra of random Lindblad operators
- Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems
- On the uniqueness of the steady-state solution of the Lindblad-Gorini-Kossakowski-Sudarshan equation
- Photon transport in a dissipative chain of nonlinear cavities
- Generating random quantum channels
- Geometry, robustness, and emerging unitarity in dissipation-projected dynamics
- Generalized Adiabatic Theorem and Strong-Coupling Limits
- Random generators of Markovian evolution: A quantum-classical transition by superdecoherence
- Asymptotics of quantum channels: conserved quantities, an adiabatic limit, and matrix product states
- On the universal constraints for relaxation rates for quantum dynamical semigroup
- Topological Protection of Coherence in a Dissipative Environment
- Uniqueness of steady states of Gorini-Kossakowski-Sudarshan-Lindblad equations: a simple proof
- Bath assisted transport in a three-site spin chain: global {\sl vs} local approach
- Asymptotics of quantum channels
- Asymptotic properties of quantum Markov chains
- Nonequilibrium photonic transport and phase transition in an array of optical cavities
- Asymptotics of quantum Markov processes: From algebraic structure to characterization of asymptotic states
- Universal Constraints on Relaxation Times for d-level GKLS master equations
- Exact steady state of the open XX-spin chain: entanglement and transport properties
- Topological Protection of Coherence in Noisy Open Quantum Systems
- Asymptotic Dynamics of Open Quantum Systems and Modular Theory
Cited by in corpus (5)
- Certifying steady-state properties of open quantum systems
- Attractor Subspace and Decoherence-Free Algebra of Quantum Dynamics
- Bath Dynamical Decoupling with a Quantum Channel
- Asymptotic dynamics in the Heisenberg picture: attractor subspace and Choi-Effros product
- A universal constraint for relaxation rates for quantum Markov generators: complete positivity and beyond