{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma",
  "title": "A Quantum Oracle Separation Between $\\mathsf{QMA}(2)$ and $\\mathsf{QMA}$",
  "canonical_statement": "We find a quantum oracle relative to which $\\mathsf{QMA}\\neq\\mathsf{QMA}(2)$. As a consequence, we resolve the no-disentanglers conjecture of Watrous: for every $\\varepsilon+\\delta<1$, any $(\\varepsilon,\\delta)$-disentangler requires input size exponential in the number of output qubits.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "resolved",
  "solution_events": [
    {
      "id": "vibemathed:a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma:event",
      "problem_id": "vibemathed:a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-09-02T00:00:00.000Z",
      "title": "arXiv",
      "summary": "The authors construct a unitary oracle $U$ such that\n$$\n\\mathsf{QMA}^{U}\\neq\\mathsf{QMA}(2)^{U}.\n$$\nTheir black-box problem is solvable by a $\\mathsf{QMA}(2)$ verifier with one oracle query and linear-size unentangled proofs, whereas any $\\mathsf{QMA}$ verifier must use either exponentially many queries or an exponentially large witness.\n\nAs a non-oracle consequence, they prove that for every fixed $\\varepsilon,\\delta\\ge 0$ with $\\varepsilon+\\delta<1$, any $(\\varepsilon,\\delta)$-disentangler requires exponentially many input qubits in the number of output qubits, resolving Watrous's no-disentanglers conjecture.",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma:attempt"
      ],
      "method_family_ids": [
        "vibemathed:a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma:method"
      ],
      "source_assertion_ids": [
        "vibemathed:a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma:attempt",
      "problem_id": "vibemathed:a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma",
      "model": "ChatGPT 5.6 Sol",
      "provider": "OpenAI",
      "attempted_at": "2026-09-02T00:00:00.000Z",
      "human_collaborators": [
        "John Bostanci; Sabee Grewal; Jonas Haferkamp; Andrew Huang; Yeongwoo Hwang; Anand Natarajan; Chinmay Nirkhe"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The authors explicitly state that the proof idea underlying the main theorem was generated using ChatGPT 5.6 Sol. They initially directed Sol to the unitary polynomial method of She and Yuen; with minimal further guidance, the model proposed the proof idea used in the paper. The authors then verified, simplified, and developed the argument. The key construction uses symmetric and antisymmetric subspace projectors to make the relevant local-unitary invariant polynomials collapse to a single univariate polynomial, reducing the lower bound to the approximate degree of $\\mathrm{OR}$.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Aaronson, Beigi, Drucker, Fefferman and Shor, The Power of Unentanglement, where the question is posed",
          "url": "https://arxiv.org/abs/0804.0802",
          "kind": "problem-record",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2609.02865",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: A Quantum Oracle Separation Between $\\mathsf{QMA}(2)$ and $\\mathsf{QMA}$",
          "url": "https://vibemathed.com/problem/a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma:verification",
      "problem_id": "vibemathed:a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma",
      "solution_event_id": "vibemathed:a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Unreviewed. A 25-page preprint two days old, no peer review, no formalisation. Seven authors, including several who work on exactly this, state that they \"verified, simplified, and developed\" the model's proof idea and take full responsibility. The argument reduces to the approximate degree of OR through the She-Yuen unitary polynomial method, so it is checkable by anyone who knows that toolkit. Nobody outside the author list has done so on the record.",
      "sources": [
        {
          "label": "VibeMathed: A Quantum Oracle Separation Between $\\mathsf{QMA}(2)$ and $\\mathsf{QMA}$",
          "url": "https://vibemathed.com/problem/a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2609.02865",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv",
      "url": "https://arxiv.org/abs/2609.02865",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: A Quantum Oracle Separation Between $\\mathsf{QMA}(2)$ and $\\mathsf{QMA}$",
      "url": "https://vibemathed.com/problem/a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma:signal:watch_only",
      "problem_id": "vibemathed:a-quantum-oracle-separation-between-mathsf-qma-2-and-mathsf-qma",
      "kind": "watch_only",
      "reason": "Current public evidence does not meet the default replay threshold.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "uncertainties": [
    "VibeMath has not independently verified the mathematical claim.",
    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
    "VibeMath has not independently audited the mathematical statement, proof, or novelty claim."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}