{"paper":{"title":"The Existence of Diagonal Quantum Latin Squares with Maximum Cardinality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lin Huang, Yang Li","submitted_at":"2026-06-26T06:36:51Z","abstract_excerpt":"A quantum Latin square of order \\(n\\), denoted by \\(\\operatorname{QLS}(n)\\), is an \\(n \\times n\\) square whose entries are unit column vectors in the \\(n\\)-dimensional Hilbert space \\(\\mathcal{H}_n\\), such that each row and each column forms an orthonormal basis of \\(\\mathcal{H}_n\\). The cardinality of a QLS($n$) is the number of distinct vectors up to a global phase in the array. A \\(\\mathrm{QLS}(n)\\) whose main diagonal and anti-diagonal each forms an orthonormal basis of \\(\\mathcal{H}_n\\) is called a diagonal quantum Latin square (\\(\\mathrm{DQLS}(n)\\)). In this paper, we focus on the existe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27758","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/2606.27758/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"}