Information gain in quantum continual measurements

We speak of quantum continuous measurements when a quantum system is taken under observation with continuity in time and the output is not a single random variable, but rather a stochastic process. The aim of this paper is to quantify, by means of entropic quantities, the effectiveness of a continual measurement in extracting information from the underlying quantum system. Inspired by works on information transmission through quantum channels, we propose the use of a couple of mutual entropies to quantify the efficiency of continuous measurement schemes in extracting information on the measured quantum system. Properties of these measures of information are studied and bounds on them are derived.