{
  "abstract": "We prove quantum soundness of the total-degree diagonal line-vs-point test using the individual-degree soundness theorem of Ji, Natarajan, Vidick, Wright, and Yuen. A random change of coordinates yields projective polynomial decoders of total degree at most $md$. The uniform-line slice of the test bounds the weight of outcomes of degree greater than $d$, which are removed by a common relabeling. This reduction does not yield a dimension-independent soundness bound: the $\\operatorname{poly}(m)$ dependence of the individual-degree theorem persists, as discussed in Section 1.2 of arXiv:2009.12982.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27129",
  "author_total": 3,
  "authors": [
    {
      "name": "Honghao Fu"
    },
    {
      "name": "Nengkun Yu"
    },
    {
      "name": "Tianrun Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fsktbkqy8k7zr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27129",
  "fulltext_url": null,
  "id": "fsktbkqy8k7zr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27129",
  "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": "W7214186350",
  "pdf_url": "https://arxiv.org/pdf/2609.27129",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fsktbkqy8k7zr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2609.27129",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27129"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Soundness of a Total-Degree Line-versus-Point Test",
  "title_text": "Quantum Soundness of a Total-Degree Line-versus-Point Test",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/fsktbkqy8k7zr",
  "venue": "arXiv",
  "versions": []
}