The intended purpose of this work is to provide the reader with a comprehensive, state-of-
the art presentation of the theory of complex Hadamard matrices, or at least report on the …

Selected ideas of statistical designs are exploited in this paper in constructions related to
Mutually Unbiased Bases (MUBs). In dimension d, MUBs are a collection of orthonormal …

Inspired by some intriguing examples, we study uniform association schemes and uniform
coherent configurations, including cometric Q-antipodal association schemes. After a review …

Maximal sets of mutually unbiased bases are useful throughout quantum physics, both in a
foundational context and for applications. To date, it remains unknown if complete sets of …

We develop a general theory of almost Hadamard matrices. These are by definition the
matrices H∈ MN (ℝ) having the property that is orthogonal, and is a local maximum of the 1 …

Construction of a large class of Mutually Unbiased Bases (MUBs) for non-prime power
composite dimensions ($ d= k\times s $) is a long standing open problem, which leads to …

In this paper, we give a new construction of parametric families of complex Hadamard
matrices of square orders, and connect them to equiangular tight frames. The results …

Balancedly splittable Hadamard matrices are introduced and studied. A connection is made
to the Hadamard diagonalizable strongly regular graphs, maximal equiangular lines set, and …

We introduce mutually unbiased complex Hadamard (MUCH) matrices and show that the
number of MUCH matrices of order 2 n, n odd, is at most 2 and the bound is attained for n …

We introduce the concept of linked systems of symmetric group divisible designs. The
connection with association schemes is established, and as a consequence we obtain an …