Continuous observation of quantum systems

In a series of papers in the 1980s Alexander Holevo proved a classification theorem for continuous quantum measurement processes, or, as they would today be called, stationary quantum trajectories in continuous time. His main tools were functional analytic in character: starting from a Bochner-type inequality he employed dilation techniques for positive definite kernels. Here, we give an alternative, more probabilistic proof: we use weak convergence of measures and employ Lévy’s Continuity Theorem. We clarify the boundedness conditions in Holevo’s theorem, and supply a simple example from quantum optics.