Systems of Imprimitivity for the Clifford Group
2014 (English)In: Quantum information & computation, ISSN 1533-7146, Vol. 14, no 3-4, 339-360 p.Article in journal (Refereed) Published
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.
Clifford group, SIC POVM, Sparse representation
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-106101ISI: 000333068200009ScopusID: 2-s2.0-84890390530OAI: oai:DiVA.org:liu-106101DiVA: diva2:714191