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dc.contributor.author
Burgarth, Daniel
dc.contributor.author
Giovannetti, Vittorio
dc.date.accessioned
2018-10-25T15:24:40Z
dc.date.available
2017-06-08T18:22:11Z
dc.date.available
2018-10-25T15:24:40Z
dc.date.issued
2007-05
dc.identifier.issn
1367-2630
dc.identifier.other
10.1088/1367-2630/9/5/150
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/8924
dc.identifier.doi
10.3929/ethz-b-000008924
dc.description.abstract
We give a simple and physically intuitive necessary and sufficient condition for a map acting on a compact metric space to be mixing (i.e. infinitely many applications of the map transfer any input into a fixed convergency point). This is a generalization of the 'Lyapunov direct method'. First we prove this theorem in topological spaces and for arbitrary continuous maps. Finally we apply our theorem to maps which are relevant in open quantum systems and quantum information, namely quantum channels. In this context, we also discuss the relations between mixing and ergodicity (i.e. the property that there exists only a single input state which is left invariant by a single application of the map) showing that the two are equivalent when the invariant point of the ergodic map is pure.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Institute of Physics
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/3.0/
dc.title
The generalized Lyapunov theorem and its application to quantum channels
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 3.0 Unported
dc.date.published
2007-03-23
ethz.journal.title
New Journal of Physics
ethz.journal.volume
9
en_US
ethz.journal.abbreviated
New J. Phys.
ethz.pages.start
150
en_US
ethz.size
18 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.nebis
001997538
ethz.publication.place
London
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
03704 - Wolf, Stefan (SNF-Professur)
en_US
ethz.leitzahl.certified
03704 - Wolf, Stefan (SNF-Professur)
ethz.date.deposited
2017-06-08T18:22:23Z
ethz.source
ECIT
ethz.identifier.importid
imp59364bd0cf42f83471
ethz.ecitpid
pub:19742
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2017-07-15T01:45:12Z
ethz.rosetta.lastUpdated
2022-03-28T21:31:39Z
ethz.rosetta.versionExported
true
ethz.COinS
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