Noncommutative Equiangular Lines: van Lint-Seidel Relative and Gerzon Universal Bounds

TL;DR

This paper introduces the concept of noncommutative equiangular lines and extends classical bounds to this new setting, providing foundational results for noncommutative frame theory.

Contribution

It develops noncommutative analogues of key bounds for equiangular lines, expanding the theoretical framework in this area.

Findings

Derived noncommutative van Lint-Seidel relative bounds

Established noncommutative Gerzon universal bounds

Extended classical bounds to noncommutative setting

Abstract

We introduce the notion of noncommutative equiangular lines and derive noncommutative versions of fundamental van Lint-Seidel relative and Gerzon universal bounds.