{
  "abstract": "Marriott and Watrous showed that quantum Merlin--Arthur games admit generic error reduction without increasing witness size [Computational Complexity, 2005]. In this work, we show that this state-size-preserving amplification property does not hold for polynomial-time quantum computation with quantum advice. In particular, we present decision problems for which even a vanishing additive error reduction requires longer advice. More precisely, for every polynomially bounded advice length $m(n)\\geq n^4$ and every error bound $\\varepsilon(n)$ that stays below $1/2$ by at least an inverse polynomial, there is a positive function $δ$ with $δ(n)=O\\bigl(\\min\\{(\\log m/m)^{1/4},\\ \\sqrt{\\log m/m}\\,/(1/2-\\varepsilon(n))\\}\\bigr)$ such that $\\mathsf{BQP}_{\\varepsilon}/\\mathsf{q}m \\subsetneq \\mathsf{BQP}_{\\varepsilon + δ}/\\mathsf{q}m$; for constant $\\varepsilon$ the gap is $O(\\sqrt{\\log m/m})$. Here, $\\mathsf{BQP}_\\varepsilon/\\mathsf{q}m$ is the class of languages recognizable with error at most $\\varepsilon(n)$ by a polynomial-time quantum algorithm with an $m(n)$-qubit advice state that only depends on the input length $n$. We show this by proving a stronger separation $\\mathsf{P}_{\\varepsilon+δ}/\\mathsf{r} m \\not\\subset \\mathsf{BQP}_{\\varepsilon}/\\mathsf{q} m$, where $\\mathsf{P}_{\\varepsilon}/\\mathsf{r}m$ is the class of languages recognizable with error at most $\\varepsilon(n)$ by a deterministic polynomial-time algorithm with an $m(n)$-bit advice string sampled from a distribution that depends only on $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03377",
  "author_total": 2,
  "authors": [
    {
      "name": "Shih-Han Hung"
    },
    {
      "name": "Han-Hsuan Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/efwvsewrnv3d9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03377",
  "fulltext_url": null,
  "id": "efwvsewrnv3d9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03377",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.03377",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/efwvsewrnv3d9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03377",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03377"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "No Size-Preserving Amplification with Quantum Advice",
  "title_text": "No Size-Preserving Amplification with Quantum Advice",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:50Z",
  "url": "https://research.draconitic.com/paper/efwvsewrnv3d9",
  "venue": "arXiv",
  "versions": []
}