Stochastic Action Functionals for Diffusive Quantum Trajectories

There has recently been considerable interest in applying a stochastic action formalism to describe diffusive continuous quantum measurement processes, following [Chantasri, Dressel, and Jordan (2013)]. We compare this method to similar approaches based on the Onsager-Machlup (OM) functional, that were developed in the context of classical stochastic processes. Such a comparison of action functionals reveals surprising similarities and differences between distinct approaches, including some severe limitations of a covariant class of OM functionals with respect to quantum measurement problems. Emphasis is given to the interpretation of optimal trajectories derived from each type of action we consider.