{
  "abstract": "Relativization is concerned with comparing computational models with black-box access to an oracle. For promise problems, black-box access is not canonical due to inputs outside of the promise being unconstrained. We study two semantics for such access. Under robust queries, a machine must correctly answer regardless of the completion of the problem,, while loose access requires that the internal choices of a machine do not change based on off-promise queries. Our first result separates the language and promise settings. Namely, we construct an oracle $O$ such that $\\mathsf{P}^O = \\mathsf{BQP}^O = \\mathsf{AWPP}^O$, but $\\mathsf{PromiseBQP}^O\\not\\subseteq\\mathsf{PromiseP}^O_{\\mathsf{/poly}}$. In particular, $\\mathsf{BPP}^O = \\mathsf{BQP}^O$, but $\\mathsf{PromiseBQP}^O \\neq \\mathsf{PromiseBPP}^O$, showing that results for languages need not transfer to promises. Next, we use loose queries to strengthen the upper bound on the Quantum-Classical Polynomial Hierarchy from $\\mathsf{P}^{\\mathsf{PP}^{\\mathsf{PP}}}$ to $\\mathsf{QCPH} \\subseteq \\mathsf{BP\\cdot PP} \\subseteq \\mathsf{PromiseBPP}^{\\mathsf{PP}}$. The same proof also shows $\\mathsf{PP}^\\mathsf{PromiseBQP} = \\mathsf{PP}$. Additionally, we show that $\\mathsf{PromiseBQP}$, even when given quantum advice, is self-low under robust queries. Finally, we exhibit an obstruction to transferring language-level counting results to promise classes. Although $\\mathsf{AWPP}$ and $\\mathsf{APP}$ are low for $\\mathsf{PP}$, a corresponding promise analogue would collapse the counting hierarchy as $\\mathsf{GapP} \\subseteq \\mathsf{FP}^{\\mathsf{PromiseAWPP}}$. This motivates the introduction of $\\mathsf{PromisePostBQP^*}$, which restricts $\\mathsf{PostBQP}$ to input-indepencent postselection. By showing that it is low for \\PP, we obtain $\\mathsf{PP}^{\\mathsf{PromiseYQP^*}} = \\mathsf{PP}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07945",
  "author_total": 3,
  "authors": [
    {
      "name": "David Miloschewsky"
    },
    {
      "name": "Supartha Podder"
    },
    {
      "name": "Dorian Rudolph"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4vypn8qegxjy2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07945",
  "fulltext_url": null,
  "id": "4vypn8qegxjy2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07945",
  "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": "W7211990334",
  "pdf_url": "https://arxiv.org/pdf/2609.07945",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4vypn8qegxjy2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.07945",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07945"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Promises should be taken seriously: On relativization with promise problems",
  "title_text": "Promises should be taken seriously: On relativization with promise problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/4vypn8qegxjy2",
  "venue": "arXiv",
  "versions": []
}