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

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.
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01267109
Contributor : Nina Amini <>
Submitted on : Wednesday, February 3, 2016 - 9:36:37 PM
Last modification on : Wednesday, September 16, 2020 - 4:46:09 PM

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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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