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
Document type :
Journal articles
Complete list of metadatas
https://hal-centralesupelec.archives-ouvertes.fr/hal-01267109
Contributor : Nina Amini <>
Submitted on : Wednesday, February 3, 2016 - 9:36:37 PM
Last modification on : Friday, December 20, 2019 - 11:48:03 AM

Links full text

openaccess

Identifiers

Collections

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

Citation

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⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

318

Contact

Informations

CCSD