dorsal/arxiv
View SchemaConstructions of complex Hadamard matrices via tiling Abelian groups
| Authors | Máté Matolcsi, Júlia Réffy, Ferenc Szöllősi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0607073 |
| URL | https://arxiv.org/abs/quant-ph/0607073 |
Abstract
Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling Abelian groups and constructions of complex Hadamard matrices. First, we recover a recent very general construction of complex Hadamard matrices due to Dita via a natural tiling construction. Then we find some necessary conditions for any given complex Hadamard matrix to be equivalent to a Dita-type matrix. Finally, using another tiling construction, due to Szabo, we arrive at new parametric families of complex Hadamard matrices of order 8, 12 and 16, and we use our necessary conditions to prove that these families do not arise with Dita's construction. These new families complement the recent catalogue of complex Hadamard matrices of small order.
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"abstract": "Applications in quantum information theory and quantum tomography have raised\ncurrent interest in complex Hadamard matrices. In this note we investigate the\nconnection between tiling Abelian groups and constructions of complex Hadamard\nmatrices. First, we recover a recent very general construction of complex\nHadamard matrices due to Dita via a natural tiling construction. Then we find\nsome necessary conditions for any given complex Hadamard matrix to be\nequivalent to a Dita-type matrix. Finally, using another tiling construction,\ndue to Szabo, we arrive at new parametric families of complex Hadamard matrices\nof order 8, 12 and 16, and we use our necessary conditions to prove that these\nfamilies do not arise with Dita\u0027s construction. These new families complement\nthe recent catalogue of complex Hadamard matrices of small order.",
"arxiv_id": "quant-ph/0607073",
"authors": [
"M\u00e1t\u00e9 Matolcsi",
"J\u00falia R\u00e9ffy",
"Ferenc Sz\u00f6ll\u0151si"
],
"categories": [
"quant-ph"
],
"title": "Constructions of complex Hadamard matrices via tiling Abelian groups",
"url": "https://arxiv.org/abs/quant-ph/0607073"
},
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