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arxiv: 1102.1268 · v2 · pith:2SWDDZEXnew · submitted 2011-02-07 · 🪐 quant-ph · math-ph· math.MP

The monomial representations of the Clifford group

D.M. Appleby , Ingemar Bengtsson , Stephen Brierley , Markus Grassl , David Gross , Jan-{\AA}ke Larsson This is my paper
classification 🪐 quant-ph math-phmath.MP
keywords groupclifforddimensionmonomialsicsapplicationsbasesexact
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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.

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