  The fidelity between the state of a continuously observed quantum system and
the state of its associated quantum filter, is shown to be always a
submartingale. The observed system is assumed to be governed by a
continuous-time Stochastic Master Equation (SME), driven simultaneously by
Wiener and Poisson processes and that takes into account incompleteness and
errors in measurements. This stability result is the continuous-time
counterpart of a similar stability result already established for discrete-time
quantum systems and where the measurement imperfections are modeled by a left
stochastic matrix.
