The monomial representations of the Clifford group

Appleby, D. M.Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada (author)

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||
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.

Bengtsson, IngemarStockholms universitet,Fysikum,Stockholms Universitet, AlbaNova, Fysikum, Stockholm, Sweden(Swepub:su)ibeng (author)
Brierley, StephenDepartment of Mathematics, University of Bristol, UK (author)
Grassl, MarkusCentre for Quantum Technologies, National University of Singapore, Singapore (author)
Gross, DavidInstitute for Theoretical Physics, ETH Zürich, 8093 Züurich, Switzerland (author)
Larsson, Jan-ÅkeLinköpings universitet,Informationskodning,Tekniska högskolan(Swepub:liu)janla64 (author)
Perimeter Institute for Theoretical Physics, Waterloo, Ontario, CanadaFysikum (creator_code:org_t)

In:Quantum information & computation: Rinton Press, Inc.12:5-6, s. 404-4311533-7146

By the author/editor: Appleby, D. M.; Bengtsson, Ingem ...; Brierley, Stephe ...; Grassl, Markus; Gross, David; Larsson, Jan-Åke

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