Attractor Subspace and Decoherence-Free Algebra of Quantum Dynamics

Abstract: In this review we discuss some results on the asymptotic dynamics of finite-dimensional open quantum systems in the Heisenberg picture. Both the spectral and algebraic approaches to this topic are addressed, with particular emphasis on their relationship. The analysis is conducted in both the discrete-time and the continuous-time Markovian settings. In the final part of the work, some issues emerging in the infinite-dimensional case are also discussed. In particular, we provide an example of a Markovian evolution whose decoherence-free algebra is a type III von Neumann algebra.