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On stability of continuous-time quantum filters

Abstract : 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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Submitted on : Wednesday, March 28, 2012 - 6:08:04 PM
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Hadis Amini, Mazyar Mirrahimi, Pierre Rouchon. On stability of continuous-time quantum filters. 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) 2011, Dec 2011, Orlando, United States. pp.6242 - 6247, ⟨10.1109/CDC.2011.6160631⟩. ⟨hal-00683468⟩



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