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Article: Induced metric and matrix inequalities on unitary matrices

TitleInduced metric and matrix inequalities on unitary matrices
Authors
Chau, HFLi, CKPoon, YTSze, NS
Issue Date2012
PublisherInstitute of Physics Publishing Ltd. The Journal's web site is located at http://iopscience.iop.org/1751-8121/
Citation
Journal Of Physics A: Mathematical And Theoretical, 2012, v. 45 n. 9, article no. 095201 How to Cite?
DOI: http://dx.doi.org/10.1088/1751-8113/45/9/095201
AbstractRecently, Chau (2011 Quantum Inform. Comput. 11 721) showed that one can define certain metrics and pseudo-metrics on U(n), the group of all n × n unitary matrices, based on the arguments of the eigenvalues of the unitary matrices. More importantly, these metrics and pseudo-metrics have quantum information theoretical meanings. So it is instructive to study this kind of metrics and pseudo-metrics on U(n). Here we show that any symmetric norm on ℝ n induces a metric on U(n). Furthermore, using the same technique, we prove an inequality concerning the eigenvalues of a product of two unitary matrices which generalizes a few inequalities obtained earlier by Chau (arXiv:1006.3614v1). © 2012 IOP Publishing Ltd.
Persistent Identifierhttp://hdl.handle.net/10722/145919
ISSN
1751-8113
2021 Impact Factor: 2.331
2020 SCImago Journal Rankings: 0.787
ISI Accession Number ID
WOS:000300777100006
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorChau, HFen_HK
dc.contributor.authorLi, CKen_HK
dc.contributor.authorPoon, YTen_HK
dc.contributor.authorSze, NSen_HK
dc.date.accessioned2012-03-27T09:02:06Z-
dc.date.available2012-03-27T09:02:06Z-
dc.date.issued2012en_HK
dc.identifier.citationJournal Of Physics A: Mathematical And Theoretical, 2012, v. 45 n. 9, article no. 095201en_HK
dc.identifier.issn1751-8113en_HK
dc.identifier.urihttp://hdl.handle.net/10722/145919-
dc.description.abstractRecently, Chau (2011 Quantum Inform. Comput. 11 721) showed that one can define certain metrics and pseudo-metrics on U(n), the group of all n × n unitary matrices, based on the arguments of the eigenvalues of the unitary matrices. More importantly, these metrics and pseudo-metrics have quantum information theoretical meanings. So it is instructive to study this kind of metrics and pseudo-metrics on U(n). Here we show that any symmetric norm on ℝ n induces a metric on U(n). Furthermore, using the same technique, we prove an inequality concerning the eigenvalues of a product of two unitary matrices which generalizes a few inequalities obtained earlier by Chau (arXiv:1006.3614v1). © 2012 IOP Publishing Ltd.en_HK
dc.languageengen_US
dc.publisherInstitute of Physics Publishing Ltd. The Journal's web site is located at http://iopscience.iop.org/1751-8121/en_US
dc.relation.ispartofJournal of Physics A: Mathematical and Theoreticalen_HK
dc.rightsJournal of Physics A: Mathematical and Theoretical. Copyright © Institute of Physics Publishing Ltd.-
dc.titleInduced metric and matrix inequalities on unitary matricesen_HK
dc.typeArticleen_HK
dc.identifier.emailChau, HF: hfchau@hku.hken_HK
dc.identifier.authorityChau, HF=rp00669en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1088/1751-8113/45/9/095201en_HK
dc.identifier.scopuseid_2-s2.0-84863183219en_HK
dc.identifier.hkuros198814en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84863183219&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume45en_HK
dc.identifier.issue9en_HK
dc.identifier.eissn1751-8121-
dc.identifier.isiWOS:000300777100006-
dc.identifier.scopusauthoridChau, HF=7005742276en_HK
dc.identifier.scopusauthoridLi, CK=8048590800en_HK
dc.identifier.scopusauthoridPoon, YT=7006219378en_HK
dc.identifier.scopusauthoridSze, NS=7003280174en_HK
dc.customcontrol.immutablejt 130418-
dc.identifier.issnl1751-8113-

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