{
  "annotation_id": "9304f764-fab4-4bd9-bc6a-a5a42fef4f49",
  "date_created": "2026-03-02T18:02:27.567000Z",
  "date_modified": "2026-03-02T18:02:27.567000Z",
  "file_hash": "86f947efa6b388e2f406de4b7b6ae7f2b411ff65ad7c15cf925fd348e77d5a1c",
  "private": false,
  "record": {
    "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"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3e0cd318-a971-4416-950f-8aa3bb5e1e86",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}