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dc.contributor.authorTeo, Colin
dc.contributor.authorCombes, Joshua
dc.contributor.authorWiseman, Howard M
dc.date.accessioned2017-09-05T00:34:46Z
dc.date.available2017-09-05T00:34:46Z
dc.date.issued2014
dc.identifier.issn1367-2630
dc.identifier.doi10.1088/1367-2630/16/10/105010
dc.identifier.urihttp://hdl.handle.net/10072/124583
dc.description.abstractIt was first shown by Jacobs, in 2003, that the process of qubit state purification by continuous measurement of one observable can be enhanced, on average, by unitary feedback control. Here, we quantify this by the reduction in any one of the family of R鮹i entropies ${{S}_{/alpha }}$, with $0/lt /alpha /lt /infty $, at some terminal time, revealing the rich structure of stochastic quantum control even for this simple problem. We generalize Jacobs' original argument, which was for the (unique) impurity measure with a linear evolution map under his protocol, by replacing linearity with convexity, thereby making it applicable to R鮹i entropies ${{S}_{/alpha }}$ for a in a finite interval about one. Even with this generalization, Jacobs' argument fails to identify the surprising fact, which we prove by Bellman's principle of dynamic programming, that his protocol is globally optimal for all R鮹i entropies whose decrease is locally maximized by that protocol. Also surprisingly, even though there is a range of R鮹i entropies whose decrease is always locally maximized by the null-control protocol, that null-control protocol cannot be shown to be globally optimal in any instance. These results highlight the non-intuitive relation between local and global optimality in stochastic quantum control.
dc.description.peerreviewedYes
dc.languageEnglish
dc.publisherInstitute of Physics Publishing
dc.publisher.placeUnited Kingdom
dc.relation.ispartofpagefrom105010-1
dc.relation.ispartofpageto105010-17
dc.relation.ispartofjournalNew Journal of Physics
dc.relation.ispartofvolume16
dc.subject.fieldofresearchQuantum Information, Computation and Communication
dc.subject.fieldofresearchPhysical Sciences
dc.subject.fieldofresearchcode020603
dc.subject.fieldofresearchcode02
dc.titleGlobal versus local optimality in feedback-controlled qubit purification: new insights from minimizing Rényi entropies
dc.typeJournal article
dc.type.descriptionC1 - Articles
dc.type.codeC - Journal Articles
dcterms.licensehttp://creativecommons.org/licenses/by/3.0/
dc.description.versionPublished
gro.rights.copyright© The Author(s) 2014. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
gro.hasfulltextFull Text
gro.griffith.authorWiseman, Howard M.
gro.griffith.authorCombes, Joshua LA.
gro.griffith.authorTeo, Colin


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