Stability analysis of quantum systems: A Lyapunov criterion and an invariance principle

In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In analog to the classical probability measure for Markovian processes, we show that the set of invariant density operators is both closed and convex. We then show how to analyze the stability of this set via a candidate Lyapunov operator. We complete our analysis of the set of invariant density operators by introducing an analog of the Barbashin–Krasovskii–LaSalle theorem on the dynamics of quantum systems.