arXiv subjects

Bengt R. Karlsson

Publications and source records attributed to Bengt R. Karlsson.

4 recordsLinked to original sources

arXiv2016

$BCCB$ complex Hadamard matrices of order 9, and MUBs

A new type of complex Hadamard matrices of order 9 are constructed. The studied matrices are symmetric, block circulant with circulant blocks ($BCCB$) and form an until now unknown non-reducible and non-affine two-parameter orbit. Several suborbits are identified, including a one-parameter intersection with the Fourier orbit $F_{9}^{(4)}$. The defect of this new type of Hadamard matrices is observed to vary, from a generic value 2 to the anomalous values 4 and 10 for some sub-orbits, and to 12 and 16 for some single matrices. The latter matrices are shown to be related to complete sets of MUBs in dimension 9.

quant-ph↗

arXiv2010

H_2-reducible Hadamard matrices of order 6

Complex Hadamard matrices H of order 6 are characterized in a novel manner, according to the presence/absence of order 2 Hadamard submatrices. It is shown that if there exists one such submatrix, H is equivalent to a Hadamard matrix where all the nine submatrices are Hadamard. The ensuing subset of H_2-reducible complex Hadamard matrices is more general than might be thought, and, significantly, includes all the up till now described (one- and two-parameter) families of order 6. A known, isolated matrix, and most numerically generated matrices, fall outside the subset.

math-ph↗

arXiv2010

Threeparameter complex Hadamard matrices of order 6

A three-parameter family of complex Hadamard matrices of order 6 is presented. It significantly extends the set of closed form complex Hadamard matrices of this order, and in particular contains all previously described one- and two-parameter families as subfamilies.

math-ph↗

arXiv2009

Two-parameter complex Hadamard matrices for N=6

A new, two-parameter, nonaffine family of complex Hadamard matrices of order 6 is reported. It interpolates between the two Fourier families, and contains as one-parameter subfamilies the Dita family, a symmetric family and an almost (up to equivalence) self-adjoint family.

math-ph↗