2011/02/28 by D. M. Appleby, Ingemar Bengtsson, Stephen Brierley +4 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Circulant matrix #Clifford algebra #Combinatorics #Dimension (graph theory) #Discrete mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group (periodic table) #Heisenberg group #Mathematics #Monomial #Permutation (music) #Permutation matrix #Physics #Pure mathematics #Quantum mechanics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.26421/qic12.5-6-3
published as Quantum Information and Computation, Vol. 12 No. 5&6, 0404-0431 (2012) · Additional author and exact solutions to the SIC problem in dimension 16 added
arxiv created 2011/08/25 · openalex publication_date 2012/05/01 · arxiv updated 2022/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.