On stability of continuous-time quantum filters

H. Amini; M. Mirrahimi; P. Rouchon

doi:10.1109/CDC.2011.6160631

On stability of continuous-time quantum filters

H. Amini, M. Mirrahimi, P. Rouchon

École Polytechnique

Mines ParisTech

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6242-6247
Number of pages	6
ISBN (Print)	9781612848006
DOIs	https://doi.org/10.1109/CDC.2011.6160631
Publication status	Published - 1 Jan 2011
Event	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States Duration: 12 Dec 2011 → 15 Dec 2011

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country/Territory	United States
City	Orlando, FL
Period	12/12/11 → 15/12/11

Access to Document

10.1109/CDC.2011.6160631

Cite this

Amini, H., Mirrahimi, M., & Rouchon, P. (2011). On stability of continuous-time quantum filters. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 6242-6247). Article 6160631 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2011.6160631

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Amini, H, Mirrahimi, M & Rouchon, P 2011, On stability of continuous-time quantum filters. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6160631, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 6242-6247, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6160631

On stability of continuous-time quantum filters. / Amini, H.; Mirrahimi, M.; Rouchon, P.
2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc., 2011. p. 6242-6247 6160631 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Mirrahimi, M.

AU - Rouchon, P.

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N2 - 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.

AB - 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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DO - 10.1109/CDC.2011.6160631

M3 - Conference contribution

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BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

Y2 - 12 December 2011 through 15 December 2011

ER -

On stability of continuous-time quantum filters

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