{
  "annotation_id": "b89e583c-d4e0-41fc-969a-fc1c6f941051",
  "date_created": "2026-02-17T05:53:20.058000Z",
  "date_modified": "2026-02-17T05:53:20.058000Z",
  "file_hash": "319da64e94c556ac38fe481b95cef1c07624521c872275304034cc473dcb8d00",
  "private": false,
  "record": {
    "abstract": "A quantum Latin square of order $n$ (denoted as QLS$(n)$) is an $n\\times n$ array whose entries are unit column vectors from the $n$-dimensional Hilbert space $\\mathcal{H}_n$, such that each row and column forms an orthonormal basis. Two unit vectors $|u\\rangle, |v\\rangle\\in \\mathcal{H}_n$ are regarded as identical if there exists a real number $\\theta$ such that $|u\\rangle=e^{i\\theta}|v\\rangle$; otherwise, they are considered distinct. The cardinality $c$ of a QLS$(n)$ is the number of distinct vectors in the array. In this note,we use sub-QLS$(6)$ to prove that for any integer $m\\geq 2$ and any $c\\in [6m,36m^2]\\setminus \\{6m+1\\}$, there is a QLS$(6m)$ with cardinality $c$.",
    "arxiv_id": "2601.09132",
    "authors": [
      "Ying Zhang",
      "Lijun Ji"
    ],
    "categories": [
      "quant-ph",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Quantum Latin squares of order $6m$ with all possible cardinalities",
    "url": "https://arxiv.org/abs/2601.09132",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "61ff5166-9a70-45e7-905e-89b70d4f1534",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}