{
  "abstract": "Generalized measurements can be implemented projectively after enlarging the Hilbert space, but this dilation changes the available local dimension. We construct a Bell functional with rational coefficients that separates the two measurement models at local dimension two. An explicit three-outcome qubit positive-operator-valued measure with rational matrix entries attains $2\\sqrt2+1/100$. On the other hand, all qubit-projective strategies are bounded by $2\\sqrt2+\\sqrt5/250+\\sqrt2/32400$, giving a fully analytic certified gap greater than $1/1000$. To our knowledge, this is the first fully analytic Bell-functional separation between qubit POVMs and qubit projective measurements over arbitrary shared two-qubit states. Lean certificate for the separation theorem is provided for completeness. Separately, an exact level-3 noncommutative sum-of-squares certificate proves that the explicit qubit strategy attains the unrestricted finite-dimensional tensor-product quantum optimum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.01317",
  "author_total": 4,
  "authors": [
    {
      "name": "Lin Zhu"
    },
    {
      "name": "Ranyiliu Chen"
    },
    {
      "name": "Xin Wang"
    },
    {
      "name": "Shenggen Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4t5jc0vekshnq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.01317",
  "fulltext_url": null,
  "id": "4t5jc0vekshnq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.01317",
  "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",
      "math.OA"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7172471409",
  "pdf_url": "https://arxiv.org/pdf/2608.01317",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4t5jc0vekshnq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.01317",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.01317"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Analytic Qubit Separation between POVMs and Projective Measurements",
  "title_text": "Analytic Qubit Separation between POVMs and Projective Measurements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/4t5jc0vekshnq",
  "venue": "arXiv",
  "versions": []
}