Block-circulant complex Hadamard matrices
نویسندگان
چکیده
A new method of obtaining a sequence isolated complex Hadamard matrices (CHM) for dimensions $N\geqslant 7$, based on block-circulant structures, is presented. We discuss, several analytic examples resulting from modification the Sinkhorn algorithm. In particular, we present orders $9$, $10$ and $11$, which elements are not roots unity, also multiparametric families order $10$. note novel connections between certain eight-dimensional provide insights towards classification CHM 7$. These contributions can find real applications in Quantum Information Theory constructions Mutually Unbiased Bases or Unitary Error Bases.
منابع مشابه
Circulant Hadamard Matrices
Note. The determinant of a circulant matrix is an example of a group determinant, where the group is the cyclic group of order n. In 1880 Dedekind suggested generalizing the case of circulants (and more generally group de terminants for abelian groups) to arbitrary groups. It was this suggestion that led Frobenius to the creation group of representation theory. See [1] and the references therein.
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2023
ISSN: ['0022-2488', '1527-2427', '1089-7658']
DOI: https://doi.org/10.1063/5.0144667