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Non-abelian Weyl commutation relations and the series product of quantum stochastic evolutions

Evans, D. Gwion; Gough, J.E.; James, Matthew

Description

We show that the series product, which serves as an algebraic rule for connecting state-based input-output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum stochastic models then corresponds to a non-abelian generalization of the Weyl commutation relation. We show that the series product gives the general rule for combining the generators of quantum stochastic evolutions using a Lie-Trotter product formula.

dc.contributor.authorEvans, D. Gwion
dc.contributor.authorGough, J.E.
dc.contributor.authorJames, Matthew
dc.date.accessioned2015-12-13T22:17:40Z
dc.identifier.issn1364-503X
dc.identifier.urihttp://hdl.handle.net/1885/71260
dc.description.abstractWe show that the series product, which serves as an algebraic rule for connecting state-based input-output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum stochastic models then corresponds to a non-abelian generalization of the Weyl commutation relation. We show that the series product gives the general rule for combining the generators of quantum stochastic evolutions using a Lie-Trotter product formula.
dc.publisherRoyal Society of London
dc.sourcePhilosophical Transactions of the Royal Society Series A
dc.subjectKeywords: Input; Quantum; Series product; Stochastic; Trotter product formula; Control; Quantum theory; Stochastic systems Control; Input; Quantum; Series product; Stochastic; Trotter product formula
dc.titleNon-abelian Weyl commutation relations and the series product of quantum stochastic evolutions
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume370
dc.date.issued2012
local.identifier.absfor010200 - APPLIED MATHEMATICS
local.identifier.ariespublicationf5625xPUB2632
local.type.statusPublished Version
local.contributor.affiliationEvans, D. Gwion, Aberystwyth University
local.contributor.affiliationGough, J.E., Aberystwyth University
local.contributor.affiliationJames, Matthew, College of Engineering and Computer Science, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage5437
local.bibliographicCitation.lastpage5451
local.identifier.doi10.1098/rsta.2011.0525
local.identifier.absseo970109 - Expanding Knowledge in Engineering
dc.date.updated2016-02-24T09:00:44Z
local.identifier.scopusID2-s2.0-84868109498
local.identifier.thomsonID000310365700015
CollectionsANU Research Publications

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