The monomanial representations of the Clifford group

D Markus Appleby, Ingemar Bengtsson, Steve Brierley, Markus Grassl, David Gross, Jan-Ake Larsson

Research output: Contribution to journalArticle (Academic Journal)peer-review


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.
Original languageEnglish
Pages (from-to)0404-0431
Number of pages28
JournalQuantum Information and Computation
Issue number5&6
Publication statusPublished - 2012


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