Nearly tight weighted 2-designs in complex projective spaces of every dimension

TL;DR

This paper presents a new construction method for small weighted projective 2-designs in complex spaces using dense Sidon sets, advancing the understanding of Zauner's conjecture.

Contribution

It introduces a novel approach leveraging dense Sidon sets to construct nearly tight weighted 2-designs in all dimensions, making progress on a longstanding conjecture.

Findings

Constructed small weighted 2-designs in complex projective spaces

Achieved quantitative progress on Zauner's conjecture

Demonstrated the effectiveness of dense Sidon sets in design construction

Abstract

We use dense Sidon sets to construct small weighted projective 2-designs. This represents quantitative progress on Zauner's conjecture.