New families of quaternionic Hadamard matrices

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-18 DOI:10.1007/s10623-024-01401-1

Santiago Barrera Acevedo, Heiko Dietrich, Corey Lionis

引用次数: 0

Abstract

A quaternionic Hadamard matrix (QHM) of order n is an \(n\times n\) matrix H with non-zero entries in the quaternions such that \(HH^*=nI_n\), where \(I_n\) and \(H^*\) denote the identity matrix and the conjugate-transpose of H, respectively. A QHM is dephased if all the entries in its first row and first column are 1, and it is non-commutative if its entries generate a non-commutative group. The aim of our work is to provide new constructions of infinitely many (non-commutative dephased) QHMs; such matrices are used by Farkas et al. (IEEE Trans Inform Theory 69(6):3814–3824, 2023) to produce mutually unbiased measurements.

查看原文本刊更多论文

新的四元哈达玛矩阵族

阶数为 n 的四元哈达玛矩阵（QHM）是一个在四元中具有非零条目的 \(n/times n\) 矩阵 H，使得 \(HH^*=nI_n\) ，其中 \(I_n\) 和 \(H^*\) 分别表示 H 的同位矩阵和共轭变换。如果一个 QHM 的第一行和第一列的所有条目都是 1，那么它就是去相的，如果它的条目产生一个非交换群，那么它就是非交换的。我们工作的目的是提供无限多（非交换去相位）QHM 的新构造；Farkas 等人（IEEE Trans Inform Theory 69(6):3814-3824, 2023）利用这些矩阵产生了互不偏倚的测量结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.