Abstract
In this paper, we focus on finite-dimensional quantum systems and give a general procedure to analyze its local reachability and local observability. We first derive the general Stratonovich equation of the quantum dynamics, which enables us to perform the analysis with conventional calculus using the Lie product and the Lie derivative. Our formula gives some physically new facts, and one of them is the following; the local evolution of a quantum state driven by the measurement back-action is restricted to a two-dimensional manifold without respect to the measured system. We lastly show the efficiencies of the results by studying an important example, the single-spin system.
