Lars Brink and SIC_POVMs

TL;DR

This paper presents a new number-theoretic construction of SIC-POVMs in certain dimensions, linking quantum information theory with deep mathematical conjectures, and shares personal insights from the author's mentorship experience.

Contribution

Introduces a novel number-theoretic method to construct SIC-POVMs in dimensions of the form n^2+3, connecting quantum measurement theory with advanced number theory.

Findings

Construction of SIC-POVMs in dimensions n^2+3

Links between quantum information and number theory

Personal account of academic mentorship and discovery

Abstract

The notion of SIC-POVMs comes from quantum information theory, and they were not on the horizon when I was Lars Brink's student in the early 80s. In the summer of 2022 I told Lars that I know how to use number theoretical insights to construct SIC-POVMs in any Hilbert space of dimension $n^2+3$, and that the construction provides a geometric setting for some deep number theoretical conjectures. I will give a sketch of this development, of what it was like to be Lars' student, and of what his reaction to our construction was.