酉Fourier矩阵Kronecker积的置换等价类
Permutation Equivalence Classes of Kronecker Products of Unitary Fourier Matrices
摘要：
酉傅立叶矩阵的Kronecker积在用多维快速傅里叶变换求解多级循环系统中起着重要的作用。它们也是在数学和理论物理的许多问题中出现的复阿达玛（蔡林格）矩阵的特殊情况。本文的主要结果是将酉傅立叶矩阵的所有Kronecker积的集合分解为置换等价类。量子信息论中构造有限维量子系统的最大纠缠基的问题激发了选择置换等价来关联乘积。置换不等价积可以用来构造不等价的，在一定意义上的最大纠缠基。
英文摘要：
Kronecker products of unitary Fourier matrices play important role in solving multilevel circulant systems by a multidimensional Fast Fourier Transform. They are also special cases of complex Hadamard (Zeilinger) matrices arising in many problems of mathematics and theoretical physics. The main result of the paper is splitting the set of all kronecker products of unitary Fourier matrices into permutation equivalence classes. The choice of permutation equivalence to relate the products is motivated by the quantum information theory problem of constructing maximally entangled bases of finite dimensional quantum systems. Permutation inequivalent products can be used to construct inequivalent, in a certain sense, maximally entangled bases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
