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Systems of Imprimitivity for the Clifford Group
Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada.
Stockholms Universitet, AlbaNova, Fysikum, Stockholm, Sweden.
Heilbronn Institute for Mathematical Research, Department of Mathematics, University of Bristol, United Kingdom.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
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2014 (English)In: Quantum information & computation, ISSN 1533-7146, Vol. 14, no 3-4, p. 339-360Article in journal (Refereed) Published
Abstract [en]

It is known that if the dimension is a perfect square the Clifford group can be represented by monomial matrices. Another way of expressing this result is to say that when the dimension is a perfect square the standard representation of the Clifford group has a system of imprimitivity consisting of one dimensional subspaces. We generalize this result to the case of an arbitrary dimension. Let k be the square-free part of the dimension. Then we show that the standard representation of the Clifford group has a system of imprimitivity consisting of k-dimensional subspaces. To illustrate the use of this result we apply it to the calculation of SIC-POVMs (symmetric informationally complete positive operator valued measures), constructing exact solutions in dimensions 8 (hand-calculation) as well as 12 and 28 (machine-calculation).

Place, publisher, year, edition, pages
Rinton Press , 2014. Vol. 14, no 3-4, p. 339-360
Keywords [en]
Clifford group, SIC POVM, Sparse representation
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-106101ISI: 000333068200009Scopus ID: 2-s2.0-84890390530OAI: oai:DiVA.org:liu-106101DiVA, id: diva2:714191
Available from: 2014-04-25 Created: 2014-04-24 Last updated: 2018-09-05Bibliographically approved

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Ericsson, ÅsaLarsson, Jan-Åke

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  • sv-SE
  • Other locale
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Output format
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