The monomanial representations of the Clifford group

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

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 journal › Article (Academic Journal)

Abstract

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 language	English
Pages (from-to)	0404-0431
Number of pages	28
Journal	Quantum Information and Computation
Volume	12
Issue number	5&6
Publication status	Published - 2012

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title = "The monomanial representations of the Clifford group",

abstract = "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.",

author = "Appleby, {D Markus} and Ingemar Bengtsson and Steve Brierley and Markus Grassl and David Gross and Jan-Ake Larsson",

year = "2012",

language = "English",

volume = "12",

pages = "0404--0431",

journal = "Quantum Information and Computation",

issn = "1533-7146",

publisher = "Rinton Press Inc.",

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T1 - The monomanial representations of the Clifford group

AU - Appleby, D Markus

AU - Bengtsson, Ingemar

AU - Brierley, Steve

AU - Grassl, Markus

AU - Gross, David

AU - Larsson, Jan-Ake

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

M3 - Article (Academic Journal)

VL - 12

SP - 404

EP - 431

JO - Quantum Information and Computation

JF - Quantum Information and Computation

SN - 1533-7146

IS - 5&6

ER -