On stability of continuous-time quantum-filters
Provides a theoretical stability result for quantum filtering, relevant to quantum control and estimation communities.
The authors prove that fidelity between a quantum state and its quantum-filter state is a sub-martingale, generalizing to non-pure states. This implies stability of continuous-time quantum filters, though not asymptotic convergence.
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.