# The Number Behind the Simplest SIC–POVM

@article{Bengtsson2016TheNB, title={The Number Behind the Simplest SIC–POVM}, author={Ingemar Bengtsson}, journal={Foundations of Physics}, year={2016}, volume={47}, pages={1031-1041} }

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 given.

#### 22 Citations

SICs and Algebraic Number Theory

- Mathematics, Physics
- 2017

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… Expand

Sporadic SICs and the Exceptional Lie Algebras

- Physics, Mathematics
- 2019

Sometimes, mathematical oddities crowd in upon one another, and the exceptions to one classification scheme reveal themselves as fellow-travelers with the exceptions to a quite different taxonomy.

Fibonacci Fervour in Linear Algebra and Quantum Information Theory

- Mathematics, Physics
- 2018

This is a survey on certain results which bring about a connection between Fibonacci sequences on the one hand and the areas of matrix theory and quantum information theory, on the other.

Moment maps and Galois orbits for SIC-POVMs

- Physics, Mathematics
- 2019

The equations that define covariant SIC-POVMs are interpreted in terms of moment maps. Attention is focussed on orbits of a cyclic subgroup of a maximal torus and their images in the moment polytope.… Expand

Invariant Off-Diagonality: SICs as Equicoherent Quantum States

- Physics
- 2019

Coherence, treated as a resource in quantum information theory, is a basis-dependent quantity. Looking for states that have constant coherence under canonical changes of basis yields highly symmetric… Expand

Fibonacci-Lucas SIC-POVMs

- Mathematics, Physics
- 2017

We present a conjectured family of symmetric informationally complete positive operator valued measures which have an additional symmetry group whose size is growing with the dimension. The symmetry… Expand

Quantum Theory as Symmetry Broken by Vitality

- Physics, Mathematics
- 2019

I summarize a research program that aims to reconstruct quantum theory from a fundamental physical principle that, while a quantum system has no intrinsic hidden variables, it can be understood using… Expand

The Poincaré Half-Plane for Informationally-Complete POVMs

- Computer Science, Mathematics
- Entropy
- 2018

The structure of some IC-POVMs is found to be intimately related to the Kochen–Specker theorem. Expand

The SIC Question: History and State of Play

- Computer Science, Mathematics
- Axioms
- 2017

Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 844. Expand

Triply Positive Matrices and Quantum Measurements Motivated by QBism

- Physics, Mathematics
- 2018

We study a class of quantum measurements that furnish probabilistic representations of finite-dimensional quantum theory. The Gram matrices associated with these Minimal Informationally Complete… Expand

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