Appears in collection : Observability and estimation in quantum dynamics

When continuously measuring a quantum system, one is typically interested in reconstructing the quantum state in real time as a function of the measured signal. This is natural if the objective is to control it and apply certain actions conditionally on the system state. If the objective is to estimate parameters (dynamical paramaters or detector parameters like quantum efficiencies), then reconstructing the state is not necessarily the most straightforward thing to do. Admittedly there already exists powerful parameter estimation methods that are optimal in a precise sense but like state reconstruction, they rely on a non-trivial post-processing of the signal. A crude, alternative is to see how simple and easily estimated functions of the signal depend on system/detector parameters. One may then read the parameters directly from the experimentally measured functions. This is mathematically suboptimal but easier and generally robust. A good candidate for this are n-point correlation functions of the signal. I will show how they can easily be computed (at a level of generality that, to my knowledge, has not been reached before). It will then be clear that the parameters of the system/detector can be read from them, providing a quick and dirty way to estimate them.