On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

Nina H. Amini 1, 2, 3 Zibo Miao 4 Yu Pan 4 Matthew R. James 4 Hideo Mabuchi 5
1 L2S - Laboratoire des signaux et systèmes
2 CNRS - Centre National de la Recherche Scientifique
3 CentraleSupélec
4 ANU - Australian National University - Department of engineering
5 Edward L. Ginzton Laboratory, Stanford University
Abstract : The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice.
Keywords : linear quantum stochastic differential equations (QSDEs) quantum noises Kalman filtering physical realizability linear least mean squares estimators non-commutative outputs coherent observers
Type de document :
Article dans une revue
European physical journal quantum technology, Springer, 2015, 2 (1), http://link.springer.com/article/10.1140%2Fepjqt%2Fs40507-015-0028-y. 〈10.1140/epjqt/s40507-015-0028-y〉
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01267109
Contributeur : Nina Amini <>
Soumis le : mercredi 3 février 2016 - 21:36:37
Dernière modification le : mercredi 28 novembre 2018 - 11:08:02

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INSMI | L2S | SUP_LSS | CENTRALESUPELEC | SUP_SYSTEMES | TDS-MACS | UNIV-PARIS-SACLAY

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Nina H. Amini, Zibo Miao, Yu Pan, Matthew R. James, Hideo Mabuchi. On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs. European physical journal quantum technology, Springer, 2015, 2 (1), http://link.springer.com/article/10.1140%2Fepjqt%2Fs40507-015-0028-y. 〈10.1140/epjqt/s40507-015-0028-y〉. 〈hal-01267109〉

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