Complex Equiangular Tight Frames and Erasures

TL;DR

This paper explores the differences between real and complex equiangular tight frames (ETFs), demonstrating the existence of large complex ETFs resilient to three erasures and highlighting unique properties of complex ETFs.

Contribution

It establishes the existence of large complex ETFs robust against multiple erasures and extends real ETF results to complex vector spaces, revealing fundamental differences.

Findings

Existence of arbitrarily large complex ETFs resilient to three erasures

Complex ETFs originate from a unique class

Certain real ETF results do not hold for complex ETFs

Abstract

In this paper we demonstrate that there are distinct differences between real and complex equiangular tight frames (ETFs) with regards to erasures. For example, we prove that there exist arbitrarily large non-trivial complex equiangular tight frames which are robust against three erasures, and that such frames come from a unique class of complex ETFs. In addition, we extend certain results in \cite{BP} to complex vector spaces as well as show that other results regarding real ETFs are not valid for complex ETFs.