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A quantum extended Kalman filter

Emzir, Muhammad F; Woolley, Matthew J; Petersen, Ian

Description

In quantum physics, a stochastic master equation (SME) estimates the state (density operator) of a quantum system in the Schrödinger picture based on a record of measurements made on the system. In the Heisenberg picture, the SME is a quantum filter. For a linear quantum system subject to linear measurements and Gaussian noise, the dynamics may be described by quantum stochastic differential equations (QSDEs), also known as quantum Langevin equations, and the quantum filter reduces to a...[Show more]

dc.contributor.authorEmzir, Muhammad F
dc.contributor.authorWoolley, Matthew J
dc.contributor.authorPetersen, Ian
dc.date.accessioned2021-04-30T01:11:15Z
dc.identifier.issn1751-8113
dc.identifier.urihttp://hdl.handle.net/1885/231165
dc.description.abstractIn quantum physics, a stochastic master equation (SME) estimates the state (density operator) of a quantum system in the Schrödinger picture based on a record of measurements made on the system. In the Heisenberg picture, the SME is a quantum filter. For a linear quantum system subject to linear measurements and Gaussian noise, the dynamics may be described by quantum stochastic differential equations (QSDEs), also known as quantum Langevin equations, and the quantum filter reduces to a so-called quantum Kalman filter. In this article, we introduce a quantum extended Kalman filter (quantum EKF), which applies a commutative approximation and a time-varying linearization to systems of nonlinear QSDEs. We will show that there are conditions under which a filter similar to a classical EKF can be implemented for quantum systems. The boundedness of estimation errors and the filtering problem with 'state-dependent' covariances for process and measurement noises are also discussed. We demonstrate the effectiveness of the quantum EKF by applying it to systems that involve multiple modes, nonlinear Hamiltonians, and simultaneous jump-diffusive measurements.
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherIOP Electronic Journals
dc.rights© 2017 IOP Publishing Ltd Printed in the UK
dc.sourceJournal of Physics A: Mathematical and Theoretical
dc.subjectquantum filtering
dc.subjectstochastic master equation
dc.subjecthomodyne detection and photon counting
dc.subjectKalman filter
dc.subjectextended Kalman filter
dc.titleA quantum extended Kalman filter
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume50
dc.date.issued2017
local.identifier.absfor020502 - Lasers and Quantum Electronics
local.identifier.ariespublicationa383154xPUB7329
local.publisher.urlhttp://iopscience.iop.org/1751-8121
local.type.statusPublished Version
local.contributor.affiliationEmzir, Muhammad F, University of New South Wales, Canberra
local.contributor.affiliationWoolley, Matthew J, University of NSW
local.contributor.affiliationPetersen, Ian, College of Engineering and Computer Science, ANU
local.description.embargo2099-12-31
local.bibliographicCitation.issue22
local.bibliographicCitation.startpage1
local.bibliographicCitation.lastpage25
local.identifier.doi10.1088/1751-8121/aa6e5e
local.identifier.absseo970109 - Expanding Knowledge in Engineering
dc.date.updated2020-11-23T10:07:48Z
local.identifier.scopusID2-s2.0-85019493380
local.identifier.thomsonID000408275900001
CollectionsANU Research Publications

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