{
  "abstract": "While quantum interactive proof systems using at least three messages can achieve perfect completeness, as shown by Kitaev and Watrous (STOC 2000), whether perfect completeness is achievable for one- and two-message quantum proof systems has remained open. For the one-message case, whether $\\sf QMA$ can achieve perfect completeness was posed as an open problem in Watrous (FOCS 2000) and Aharonov and Naveh (2002); for the two-message case, the corresponding problems were (implicitly) posed in Jain, Upadhyay, and Watrous~(FOCS 2009) and Kobayashi, Le Gall, and Nishimura (SICOMP, 2019). In this work, we establish that ${\\sf QIP}(2)$, ${\\rm qq}\\text{-}{\\sf QAM}$, $\\sf QAM$, and $\\sf QMA$ can achieve perfect completeness. Here ${\\rm qq}\\text{-}{\\sf QAM}$ denotes the class of promise problems admitting two-message quantum-public-coin quantum interactive proof systems in which the verifier's only message consists of half-EPR pairs. Our main technical contributions are the follows: 1. For $\\sf QMA$ (and directly for $\\sf QAM$), an exactly constructible block-encoded matrix whose kernel certifies yes instances, constructed from the acceptance operator induced by the verification circuit. This also yields an alternative proof of ${\\sf QCMA}={\\sf QCMA}_1$. 2. For ${\\sf QIP}(2)$ (and implicitly ${\\rm qq}\\text{-}{\\sf QAM}$), a new turn-halving transformation that preserves completeness and ensures that the resulting proof system retains at least two messages, provided that the terminal state before the final measurement is efficiently preparable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15926",
  "author_total": 2,
  "authors": [
    {
      "name": "Yupan Liu"
    },
    {
      "name": "Thomas Vidick"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5vpnkvdswwk8p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15926",
  "fulltext_url": null,
  "id": "5vpnkvdswwk8p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15926",
  "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": "W7213345951",
  "pdf_url": "https://arxiv.org/pdf/2609.15926",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5vpnkvdswwk8p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2609.15926",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15926"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Achieving perfect completeness for one- and two-message quantum proof systems",
  "title_text": "Achieving perfect completeness for one- and two-message quantum proof systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:36Z",
  "url": "https://research.draconitic.com/paper/5vpnkvdswwk8p",
  "venue": "arXiv",
  "versions": []
}