Detailing the equivalence between real equiangular tight frames and certain strongly regular graphs

TL;DR

This paper explores the relationship between real equiangular tight frames and strongly regular graphs, providing new techniques to understand their equivalence, with plans to extend this theory further.

Contribution

It introduces alternative methods for analyzing the equivalence between real ETFs and strongly regular graphs, paving the way for broader generalizations.

Findings

New techniques for understanding ETF and strongly regular graph equivalence

Clarification of the existing relationship between real ETFs and strongly regular graphs

Foundation for future generalizations of the theory

Abstract

An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. They arise in numerous applications. It is well known that real ETFs are equivalent to a certain subclass of strongly regular graphs. In this note, we give some alternative techniques for understanding this equivalence. In a later document, we will use these techniques to further generalize this theory.