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The monomial representations of the Clifford group
Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada.
Stockholms Universitet, AlbaNova, Fysikum, Stockholm, Sweden.
Department of Mathematics, University of Bristol, UK.
Centre for Quantum Technologies, National University of Singapore, Singapore.
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2012 (English)In: Quantum information & computation, ISSN 1533-7146, Vol. 12, no 5-6, p. 404-431Article in journal (Refereed) Published
Abstract [en]

We show that the Clifford group-the normaliser of the Weyl-Heisenberg group-can be represented by monomial phase-permutation matrices if and only if the dimension is a square number. This simplifies expressions for SIC vectors, and has other applications to SICs and to Mutually Unbiased Bases. Exact solutions for SICs in dimension 16 are presented for the first time.

Place, publisher, year, edition, pages
Rinton Press, Inc. , 2012. Vol. 12, no 5-6, p. 404-431
Keywords [en]
Clifford group, SIC POVM, Representation
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-78577ISI: 000304380700003OAI: oai:DiVA.org:liu-78577DiVA, id: diva2:534159
Note

Funding Agencies|U. S. Office of Naval Research|N00014-09-1-0247|Government of Canada through Industry Canada||Province of Ontario through the Ministry of Research Innovation||Swedish Research Council|VR 621-2007-4060|EU|212008|Institut Mittag-Leffler (Djursholm, Sweden)||German Science Foundation (DFG)|CH 843/1-1CH 843/2-1|Swiss National Science Foundation||

Available from: 2012-06-15 Created: 2012-06-15 Last updated: 2019-08-15Bibliographically approved

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Larsson, Jan-Åke

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • rtf