Sporadic SICs and the Normed Division Algebras
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.
- Publication:
-
Foundations of Physics
- Pub Date:
- August 2017
- DOI:
- 10.1007/s10701-017-0087-2
- arXiv:
- arXiv:1605.01426
- Bibcode:
- 2017FoPh...47.1060S
- Keywords:
-
- Quantum information;
- Quantum measurement;
- SIC-POVM;
- Octonions;
- E8;
- Quantum Physics
- E-Print:
- 2 pages, at the expense of deleting the definition of a Moufang loop