# SICs and Algebraic Number Theory

## TL;DR

This paper explores the intriguing links between symmetric informationally complete measurements in quantum physics and algebraic number theory, highlighting their connection to Hilbert's 12th problem, in an accessible manner for physicists.

## Contribution

It provides an accessible overview of the relationship between SIC-POVMs and algebraic number theory, emphasizing their connection to Hilbert's 12th problem.

## Key findings

- Identifies connections between SICs and algebraic number theory
- Highlights relevance to Hilbert's 12th problem
- Aims to make complex mathematics accessible to physicists

## Abstract

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.