Asymptotic dynamics in the Heisenberg picture: attractor subspace and Choi-Effros product

Abstract

We study the asymptotic dynamics of open quantum systems in the Heisenberg picture. We find an explicit expression for the attractor subspace and the dynamics that takes place in it. We present the relationship between the attractor subspaces in the Schrödinger and Heisenberg pictures and, in particular, the connection between their algebraic structures. An unfolding theorem of the asymptotics, as well as the fine structure of the recently introduced Choi-Effros decoherence-free algebra, are also discussed. Finally, we show how to extend all the results to the class of Schwarz maps.

arXiv comment22 pages

References in corpus (14)

• Noiseless Quantum Codes
• Preparation of Entangled States by Quantum Markov Processes
• 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
• Asymptotics of quantum channels: conserved quantities, an adiabatic limit, and matrix product states
• On the universal constraints for relaxation rates for quantum dynamical semigroup
• On period, cycles and fixed points of a quantum channel
• Asymptotic properties of quantum Markov chains
• Asymptotics of quantum channels
• Asymptotics of quantum Markov processes: From algebraic structure to characterization of asymptotic states
• Number of steady states of quantum evolutions
• Asymptotic Dynamics of Open Quantum Systems and Modular Theory
• Peripherally automorphic unital completely positive maps
• Attractor Subspace and Decoherence-Free Algebra of Quantum Dynamics