论文标题
块循环复合物hadamard矩阵
Block-Circulant Complex Hadamard Matrices
论文作者
论文摘要
提出了一种基于块状结构的尺寸$ n \ geqslant 7 $的隔离复合物矩阵（CHM）序列的新方法。我们讨论了sindhorn算法的修改产生的几个分析示例。特别是，我们提出了新的孤立订单矩阵$ 9 $，$ 10 $和$ 11 $，这些元素不是团结的根源，也是几个新的多参数订单的订单$ 10 $。我们注意到某些八维矩阵之间的新颖联系，并为CHM分类为$ n \ geqslant 7 $提供了新的见解。这些贡献可以在量子信息理论和相互无偏见或单一错误基础的新家族的构造中找到真实的应用。
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.
