Quantum symmetries of Hadamard matrices

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-03-09 DOI:10.1090/tran/9153

Daniel Gromada

引用次数: 0

Abstract

We define quantum automorphisms and isomorphisms of Hadamard matrices. We show that every Hadamard matrix of size N ≥ 4 N\ge 4 has quantum symmetries and that all Hadamard matrices of a fixed size are mutually quantum isomorphic. These results pass also to the corresponding Hadamard graphs. We also define quantum Hadamard matrices acting on quantum spaces and bring an example thereof over matrix algebras.

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哈达玛矩阵的量子对称性

我们定义了哈达玛矩阵的量子自变和同构。我们证明了每个大小为 N ≥ 4 N\ge 4 的哈达玛矩阵都有量子对称性，而且所有固定大小的哈达玛矩阵都互为量子同构。这些结果也适用于相应的哈达玛图。我们还定义了作用于量子空间的量子哈达玛矩阵，并举例说明了其在矩阵代数上的作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.