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In this article we study physical realizability for a class of nonlinear quantum stochastic differential equations (QSDEs). Physical realizability is a property in which a QSDE corresponds to the dynamics of an open quantum system. We derive a sufficient and necessary condition for a nonlinear QSDE to be physically realizable. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]