Block-Circulant Complex Hadamard Matrices
Abstract
A new method of obtaining a sequence of isolated complex Hadamard matrices (CHM) for dimensions N≥slant 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≥slant 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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