Permutation Equivalence Classes of Kronecker Products of Unitary Fourier Matrices

Details Permutation Equivalence Classes of Kronecker Products of Unitary Fourier Matrices Permutation Equivalence Classes of Kronecker Products of Unitary Fourier Matrices

2005-01-14

arxiv.org/abs/math/0501233v1

Linear Algebra and its Applications, vol. 418 issues 2-3 (2006), pp. 719-736

Mathematics

Rings and Algebras

26 pages

Scientific paper

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.

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