{
  "abstract": "To prove the quantum soundness of the classical low-individual-degree test, the authors of \\cite{JNVWY20LID} defined three subtests, namely the axis-parallel lines test, the self-consistency test, and the diagonal-lines test. An interesting question is whether the diagonal-lines test can be removed. In this paper, we show that the diagonal-lines test cannot simply be removed without another compatibility mechanism. Consequently, replacing the \"conditional linear functions\" by \"coordinate deletion functions\" in the proof of MIP*=RE, as mentioned in \\cite{JNVWY20LID}, does not by itself preserve the required soundness. The authors of \\cite{JNVWY20LID} found an example that requires the diagonal-lines test when \\((m, d, q) = (2, 2, 4)\\); we give an example when \\((m, d) = (2, 2)\\) and \\(q\\) is any odd prime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12346",
  "author_total": 3,
  "authors": [
    {
      "name": "Honghao Fu"
    },
    {
      "name": "Nengkun Yu"
    },
    {
      "name": "Tianrun Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bt32c1vhte27r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12346",
  "fulltext_url": null,
  "id": "bt32c1vhte27r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12346",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212924349",
  "pdf_url": "https://arxiv.org/pdf/2609.12346",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bt32c1vhte27r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2609.12346",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12346"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Low-Individual-Degree Test Without the Diagonal-Lines Test Is Not Quantum-Sound",
  "title_text": "The Low-Individual-Degree Test Without the Diagonal-Lines Test Is Not Quantum-Sound",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/bt32c1vhte27r",
  "venue": "arXiv",
  "versions": []
}