Block-Circulant Complex Hadamard Matrices

Abstract

A new method of obtaining a sequence of isolated complex Hadamard matrices (CHM) for dimensions $N⩾7$, 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 $N⩾7$. These contributions can find real applications in Quantum Information Theory and constructions of new families of Mutually Unbiased Bases or Unitary Error Bases.

22 pages, no figures

References in corpus (4)

• A finiteness result for commuting squares of matrix algebras
• Exotic complex Hadamard matrices, and their equivalence
• Detecting Entanglement can be More Effective with Inequivalent Mutually Unbiased Bases
• Isolated Hadamard Matrices from Mutually Unbiased Product Bases

Cited by in corpus (2)

• Two-Unitary Complex Hadamard Matrices of Order $36$
• Equivalence of Complex Hadamard Matrices