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Systems of Imprimitivity for the Clifford Group
Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada.
Stockholm University, Sweden .
University of Bristol, UK.
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, 339-360 p.Article 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, 339-360 p.
Keyword [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: diva2:714191
Available from: 2014-04-25 Created: 2014-04-24 Last updated: 2017-12-05Bibliographically approved

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Ericsson, ÅsaLarsson, Jan-Åke

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