On stability of continuous-time quantum filters

Authors: H. Amini, M. Mirrahimi, P. Rouchon, 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) 2011, pp. 6242 - 6247, 12-15 Dec. 2011, Orlando, USA DOI: 10.1109/CDC.2011.6160631
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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BibTeX:
@Proceedings{,
author = {H. Amini, M. Mirrahimi, P. Rouchon},
editor = {},
title = {On stability of continuous-time quantum filters},
booktitle = {50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) 2011},
volume = {},
publisher = {},
address = {},
pages = {6242 - 6247},
year = {2011},
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.},
keywords = {}}