Decompositions of Hilbert Spaces, Stability Analysis and Convergence Probabilities for Discrete-Time Quantum Dynamical Semigroups

TL;DR

This paper analyzes the convergence and stability of discrete-time quantum dynamical semigroups, providing decompositions and formulas to determine stability, convergence speed, and limit probabilities for quantum states and subspaces.

Contribution

It introduces two Hilbert space decompositions for stability analysis and a formula for limit probability distributions in quantum dynamical semigroups.

Findings

Decompositions enable stability decision-making.

Formulas for limit probabilities of invariant subspaces.

Results applicable to quantum information processing.

Abstract

We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of uncontrolled evolutions and the engineering of controlled dynamics for quantum information processing. Our results include two Hilbert space decompositions that allow for deciding the stability of the subspace of interest and for estimating of the speed of convergence, as well as a formula to obtain the limit probability distribution for a set of orthogonal invariant subspaces.