# The monomial representations of the Clifford group

@article{Appleby2012TheMR,
title={The monomial representations of the Clifford group},
author={David Marcus Appleby and Ingemar Bengtsson and Stephen Brierley and Markus Grassl and David Gross and Jan-{\AA}ke Larsson},
journal={Quantum Inf. Comput.},
year={2012},
volume={12},
pages={404-431}
}
• Published 7 February 2011
• Mathematics
• Quantum Inf. Comput.
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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