{"paper":{"title":"Quantum Latin squares with all possible cardinalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Lijun Ji, Xin Wang, Ying Zhang","submitted_at":"2025-07-08T03:40:19Z","abstract_excerpt":"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 paper, we use sub-QLS$(4)$s to prove that for any integer $m\\geq 2$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05642","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.05642/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}