Heisenberg Picture Approach to the Stability of Quantum Markov Systems

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dc.contributor.authorPan, Yu
dc.contributor.authorAmini, Hadis
dc.contributor.authorMiao, Zibo
dc.contributor.authorGough, John
dc.contributor.authorUgrinovskii, Valery
dc.contributor.authorJames, Matthew R.
dc.date.accessioned2015-12-13T22:58:43Z
dc.date.available2015-12-13T22:58:43Z
dc.date.issued2014-06-20
dc.date.updated2016-02-24T11:36:46Z
dc.description.abstractQuantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.
dc.identifier.issn0022-2488en_AU
dc.identifier.urihttp://hdl.handle.net/1885/83436
dc.publisherAmerican Institute of Physics (AIP)
dc.rightshttp://www.sherpa.ac.uk/romeo/issn/0022-2488..."Publishers version/PDF may be used on author's personal website, institutional website or institutional repository" from SHERPA/RoMEO site (as at 14/12/15). Copyright 2014 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Mathematical Physics and may be found at https://doi.org/10.1063/1.4884300
dc.sourceJournal of Mathematical Physics
dc.titleHeisenberg Picture Approach to the Stability of Quantum Markov Systems
dc.typeJournal article
local.bibliographicCitation.issue6en_AU
local.bibliographicCitation.startpage062701en_AU
local.contributor.affiliationPan, Yu, College of Engineering and Computer Science, College of Engineering and Computer Science, Research School of Engineering, The Australian National Universityen_AU
local.contributor.affiliationAmini, Hadis, Stanford University, United States of Americaen_AU
local.contributor.affiliationMiao, Zibo, College of Engineering and Computer Science, College of Engineering and Computer Science, Research School of Engineering, The Australian National Universityen_AU
local.contributor.affiliationGough, John, University of Wales, United Kingdomen_AU
local.contributor.affiliationUgrinovskii, Valery A, University of New South Wales, ADFA, Australiaen_AU
local.contributor.affiliationJames, Matthew, College of Engineering and Computer Science, College of Engineering and Computer Science, Research School of Engineering, The Australian National Universityen_AU
local.contributor.authoremailpanyustein@yahoo.deen_AU
local.contributor.authoruidu5217005en_AU
local.description.notesImported from ARIESen_AU
local.identifier.absfor010203en_AU
local.identifier.absseo970101en_AU
local.identifier.absseo970109en_AU
local.identifier.ariespublicationU5431022xPUB88en_AU
local.identifier.citationvolume55en_AU
local.identifier.doi10.1063/1.4884300en_AU
local.identifier.scopusID2-s2.0-84929012444
local.identifier.thomsonID000338634500024
local.identifier.uidSubmittedByu3488905en_AU
local.publisher.urlhttps://www.aip.org/en_AU
local.type.statusPublished Versionen_AU

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