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arXiv · 1310.3855

The quantum algebra of partial Hadamard matrices

Teo Banica·Adam Skalski
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Abstract

A partial Hadamard matrix is a matrix $H\in M_{M\times N}(\mathbb T)$ whose rows are pairwise orthogonal. We associate to each such $H$ a certain quantum semigroup $G$ of quantum partial permutations of $\{1,...,M\}$ and study the correspondence $H\to G$. We discuss as well the relation between the completion problems for a given partial Hadamard matrix and completion problems for the associated submagic matrix $P\in M_M(M_N(\mathbb C))$, in both cases introducing certain criteria for the existence of the suitable completions.

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Teo Banica, Adam Skalski. 2013-10-14. The quantum algebra of partial Hadamard matrices. https://arxiv.org/abs/1310.3855

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