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We prove that the fidelity between the quantum state governed by a continuoustime stochastic master equation driven by a Wiener process and its associatedquantum-filter state is a sub-martingale. This result is a generalization tonon-pure quantum states where fidelity does not coincide in general with asimple Frobenius inner product. This result implies the stability of suchfiltering process but does not necessarily ensure the asymptotic convergence ofsuch quantum-filters.

On stability of continuous-time quantum-filters