Foundations of Physics

, Volume 47, Issue 8, pp 1060–1064 | Cite as

Sporadic SICs and the Normed Division Algebras

Article

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.

Keywords

Quantum information Quantum measurement SIC-POVM Octonions E8 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Physics DepartmentUniversity of Massachusetts BostonBostonUSA

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