  We prove that the fidelity between the quantum state governed by a continuous
time stochastic master equation driven by a Wiener process and its associated
quantum-filter state is a sub-martingale. This result is a generalization to
non-pure quantum states where fidelity does not coincide in general with a
simple Frobenius inner product. This result implies the stability of such
filtering process but does not necessarily ensure the asymptotic convergence of
such quantum-filters.
