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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 Ginzton Laboratory [Stanford]
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
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01267109
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Submitted on : Wednesday, February 3, 2016 - 9:36:37 PM
Last modification on : Friday, October 22, 2021 - 3:03:32 AM

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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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