dc.contributor.author Teo, Colin dc.contributor.author Combes, Joshua dc.contributor.author Wiseman, Howard M dc.date.accessioned 2017-09-05T00:34:46Z dc.date.available 2017-09-05T00:34:46Z dc.date.issued 2014 dc.identifier.issn 1367-2630 dc.identifier.doi 10.1088/1367-2630/16/10/105010 dc.identifier.uri http://hdl.handle.net/10072/124583 dc.description.abstract It 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.peerreviewed Yes dc.language English dc.publisher Institute of Physics Publishing dc.publisher.place United Kingdom dc.relation.ispartofpagefrom 105010-1 dc.relation.ispartofpageto 105010-17 dc.relation.ispartofjournal New Journal of Physics dc.relation.ispartofvolume 16 dc.subject.fieldofresearch Quantum Information, Computation and Communication dc.subject.fieldofresearch Physical Sciences dc.subject.fieldofresearchcode 020603 dc.subject.fieldofresearchcode 02 dc.title Global versus local optimality in feedback-controlled qubit purification: new insights from minimizing Rényi entropies dc.type Journal article dc.type.description C1 - Articles dc.type.code C - Journal Articles dcterms.license http://creativecommons.org/licenses/by/3.0/ dc.description.version Published 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.hasfulltext Full Text gro.griffith.author Wiseman, Howard M. gro.griffith.author Combes, Joshua LA. gro.griffith.author Teo, Colin
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