SICs and Algebraic Number Theory

@article{Appleby2017SICsAA,
  title={SICs and Algebraic Number Theory},
  author={Marcus Appleby and Steven T. Flammia and Gary McConnell and Jon T. Yard},
  journal={Foundations of Physics},
  year={2017},
  volume={47},
  pages={1042-1059}
}
We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert’s 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory. 

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The simple concept of a SIC poses a very deep problem in algebraic number theory, as soon as the dimension of Hilbert space exceeds three. A detailed description of the simplest possible example is
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