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

TL;DR

This paper investigates the long-term behavior of open quantum systems in the Heisenberg picture, providing explicit formulas for attractor subspaces, their algebraic structures, and extensions to Schwarz maps, enhancing understanding of quantum decoherence.

Contribution

It introduces explicit expressions for attractor subspaces and their algebraic structures, linking Schrödinger and Heisenberg pictures, and extends results to Schwarz maps.

Findings

Explicit attractor subspace formulas derived

Connection established between Schrödinger and Heisenberg algebraic structures

Results extended to Schwarz maps class

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 Schr\"odinger 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.