# Biangular Gabor frames and Zauner's conjecture

## TL;DR

This paper explores biangular Gabor frames as a new approach to Zauner's conjecture, aiming to establish the existence of equiangular tight frames in complex dimensions without relying solely on explicit constructions.

## Contribution

It introduces biangular Gabor frames as an alternative framework that could potentially lead to a proof of Zauner's conjecture independent of current constructive methods.

## Key findings

- Proposes biangular Gabor frames as a promising approach.
- Connects the problem to Stark conjectures.
- Suggests potential for an unconditional proof.

## Abstract

Two decades ago, Zauner conjectured that for every dimension $d$, there exists an equiangular tight frame consisting of $d^2$ vectors in $\mathbb{C}^d$. Most progress to date explicitly constructs the promised frame in various dimensions, and it now appears that a constructive proof of Zauner's conjecture may require progress on the Stark conjectures. In this paper, we propose an alternative approach involving biangular Gabor frames that may eventually lead to an unconditional non-constructive proof of Zauner's conjecture.