Asymptotics of quantum channels

Abstract

We discuss several aspects concerning the asymptotic dynamics of dicrete-time semigroups associated with a quantum channel. By using an explicit expression of the asymptotic map, which describes the action of the quantum channel on its attractor manifold, we investigate the role of permutations in the asymptotic dynamics. We show that, in general, they make the asymptotic evolution non-unitary, and they are related to the divisibility of the quantum channel. Also, we derive several results about the asymptotics of faithful and non-faithful channels, and we establish a constructive unfolding theorem for the asymptotic dynamics.

27 pages

References in corpus (5)

• Analysis of quantum semigroups with GKS--Lindblad generators II. General
• Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems
• Analysis of quantum semigroups with GKS-Lindblad generators I. Simple generators
• Decompositions of Hilbert Spaces, Stability Analysis and Convergence Probabilities for Discrete-Time Quantum Dynamical Semigroups
• Peripheral Poisson Boundary

Cited by in corpus (9)

• Uniqueness of steady states of Gorini-Kossakowski-Sudarshan-Lindblad equations: a simple proof
• Theory of Metastability in Discrete-Time Open Quantum Dynamics
• Number of steady states of quantum evolutions
• Asymptotic Dynamics of Open Quantum Systems and Modular Theory
• Bath Dynamical Decoupling with a Quantum Channel
• Attractor Subspace and Decoherence-Free Algebra of Quantum Dynamics
• Operator Algebra Generalization of a Theorem of Watrous and Mixed Unitary Quantum Channels
• Asymptotic dynamics in the Heisenberg picture: attractor subspace and Choi-Effros product
• Unital Kadison-Schwarz Maps