Block-Circulant Complex Hadamard Matrices
- URL: http://arxiv.org/abs/2204.11727v4
- Date: Tue, 23 May 2023 10:13:18 GMT
- Title: Block-Circulant Complex Hadamard Matrices
- Authors: Wojciech Bruzda
- Abstract summary: A new method of obtaining a sequence of isolated complex Hadamard matrices (CHM) for dimensions $Ngeqslant 7$ is presented.
We discuss, several analytic examples resulting from a modification of the Sinkhorn algorithm.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: A new method of obtaining a sequence of isolated complex Hadamard matrices
(CHM) for dimensions $N\geqslant 7$, based on block-circulant structures, is
presented. We discuss, several analytic examples resulting from a modification
of the Sinkhorn algorithm. In particular, we present new isolated matrices of
orders $9$, $10$ and $11$, which elements are not roots of unity, and also
several new multiparametric families of order $10$. We note novel connections
between certain eight-dimensional matrices and provide new insights towards
classification of CHM for $N\geqslant 7$. These contributions can find real
applications in Quantum Information Theory and constructions of new families of
Mutually Unbiased Bases or Unitary Error Bases.
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