Bouten, Luc and van Handel, Ramon and James, Matthew R. (2007) An Introduction to Quantum Filtering. SIAM Journal on Control and Optimization, 46 (6). pp. 2199-2241. ISSN 0363-0129. doi:10.1137/060651239. https://resolver.caltech.edu/CaltechAUTHORS:BOUsiamjco07
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Abstract
This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. We describe the quantum Itô calculus and its use in the modeling of physical systems. We use both reference probability and innovations methods to obtain quantum filtering equations for system-probe models from quantum optics.
| Item Type: | Article | ||||||
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| Additional Information: | ©2007 Society for Industrial and Applied Mathematics. Reprinted with permission. Received by the editors January 30, 2006; accepted for publication (in revised form) June 20, 2007; published electronically December 21, 2007. The research of these authors [L.B. and R.v.H.] are supported by Army Research Office grant DAAD19-03-1-0073. The first author [L.B.] is additionally supported by National Science Foundation grant PHY-0456720. The research of this author is supported by the Australian Research Council. | ||||||
| Subject Keywords: | quantum filtering; quantum probability; quantum stochastic processes | ||||||
| Issue or Number: | 6 | ||||||
| DOI: | 10.1137/060651239 | ||||||
| Record Number: | CaltechAUTHORS:BOUsiamjco07 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:BOUsiamjco07 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 9429 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Archive Administrator | ||||||
| Deposited On: | 30 Dec 2007 | ||||||
| Last Modified: | 08 Nov 2021 20:59 |
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