{
  "abstract": "Pure-state consistency problems naturally lead to quantum proof systems in which a single pure witness must satisfy many acceptance constraints. The corresponding class $\\mathsf{PureSuperQMA}$ was previously known to lie between $\\mathsf{QMA}$ and $\\mathsf{QMA}(2)$, and Kamminga and Rudolph (ITCS'26) conjectured that both containments are strict. In this paper, we prove the following surprising complexity collapses $$ \\mathsf{QMA} = \\mathsf{PureSuperQMA} = \\mathsf{PureSuperQMA}(\\text{exp}) = \\mathsf{BellPureSymQMA}(\\text{poly}) $$ Here $\\mathsf{PureSuperQMA}(\\text{exp})$ allows exponentially many checks which are uniformly indexed and efficiently generated, while requiring an inverse-polynomial violation margin and an inverse-polynomial fraction of violated checks for the NO cases. $\\mathsf{BellPureSymQMA}(\\text{poly})$ is a related model that requires the prover to give the verifier polynomially many copies of a pure state, which the verifier measures separately with logarithmic output length for each local measurement, before processing the outcomes jointly. The main technical ingredient is a dimension-free stability bound for symmetric tensor states. Our simulations use polynomially many witness registers and combine a random-pair SWAP test with a permutation-invariant lift of the original verification procedure. The key step is to show that, on the symmetric subspace, the extremal verification value is close to that of some tensor-power witness with dimension-independent error. Applying this argument to the two verification models yields both simulations. As a consequence, exact $k$-local pure-state consistency is $\\mathsf{QMA}$-complete for every fixed $k\\ge2$, and so are the corresponding exact bosonic and fermionic pure $N$-representability problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11854",
  "author_total": 6,
  "authors": [
    {
      "name": "William Gay"
    },
    {
      "name": "Fernando Granha Jeronimo"
    },
    {
      "name": "Lenny Liu"
    },
    {
      "name": "Itai Leigh"
    },
    {
      "name": "Pei Wu"
    },
    {
      "name": "Haochen Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4wsfnxs3rnk98.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11854",
  "fulltext_url": null,
  "id": "4wsfnxs3rnk98",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11854",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212318304",
  "pdf_url": "https://arxiv.org/pdf/2609.11854",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4wsfnxs3rnk98.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.11854",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11854"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "PureSuperQMA(exp) = BellPureSymQMA(poly) = QMA via Dimension-Free Bosonic Argmax",
  "title_text": "PureSuperQMA(exp) = BellPureSymQMA(poly) = QMA via Dimension-Free Bosonic Argmax",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:26Z",
  "url": "https://research.draconitic.com/paper/4wsfnxs3rnk98",
  "venue": "arXiv",
  "versions": []
}