On stability of continuous-time quantum filters

@article{Amini2011OnSO,
  title={On stability of continuous-time quantum filters},
  author={Hadis Amini and Mazyar Mirrahimi and Pierre Rouchon},
  journal={IEEE Conference on Decision and Control and European Control Conference},
  year={2011},
  pages={6242-6247}
}
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. 

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