Mutually Unbiased Weighing Matrices

TL;DR

This paper explores the properties and limitations of mutually unbiased weighing matrices, extending the concept from Hadamard matrices to more general cases in both real and complex domains.

Contribution

It introduces the study of mutually unbiased weighing matrices, analyzing their existence and bounds for small orders and weights, and examines the sharpness of key upper bounds.

Findings

Identified bounds for mutually unbiased weighing matrices in small orders.

Analyzed the sharpness of existing upper bounds.

Extended the concept of mutual unbiasedness to weighing matrices in real and complex settings.

Abstract

Inspired by the many applications of mutually unbiased Hadamard matrices, we study mutually unbiased weighing matrices. These matrices are studied for small orders and weights in both the real and complex setting. Our results make use of and examine the sharpness of a very important existing upper bound for the number of mutually unbiased weighing matrices.