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Sporadic SICs and the Normed Division Algebras

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Abstract

Symmetric informationally complete quantum measurements, or SICs, are mathematically intriguing structures, which in practice have turned out to exhibit even more symmetry than their definition requires. Recently, Zhu classified all the SICs whose symmetry groups act doubly transitively. I show that lattices of integers in the complex numbers, the quaternions and the octonions yield the key parts of these symmetry groups.

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  1. Physics Department, University of Massachusetts Boston, 100 Morrissey Blvd., Boston, MA, 02125, USA

    Blake C. Stacey

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  1. Blake C. Stacey
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Stacey, B.C. Sporadic SICs and the Normed Division Algebras. Found Phys 47, 1060–1064 (2017). https://doi.org/10.1007/s10701-017-0087-2

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