{
  "abstract": "Classically testing for the presence of anti-commuting operators on a quantum device is a critical tool underpinning recent progress in classical verification of quantum computation. While such tests can be based on cryptographic assumptions, known constructions rely on highly structured assumptions, e.g. trapdoor claw-free functions. In this work, we seek to explain this state of affairs by constructing strong cryptography from (certain forms of) classical tests of anti-commutation. In particular, we formulate the notion of a test of non-commutation (ToNC), an interactive protocol between a quantum prover and classical verifier in which the prover's final-round response is obtained by measuring one of two binary observables $P_0,P_1$ depending on the verifier's challenge bit $c$. We prove that, for a broad range of parameters, ToNC implies classical-communication key agreement (KA), and ToNC combined with one-way functions implies oblivious transfer (OT). Along the way, we develop tools for and provide the first known results on hardness amplification for post-quantum KA and OT, where communication is classical but adversaries may be quantum. In particular, we prove the following results of independent interest. - Post-quantum hard-core measure theorem: For any efficiently sampleable high-min-entropy distribution $D$ over pairs $(x,b)$ such that quantum circuits have advantage at most $δ$ in predicting $b$ from $x$, there exists a sub-distribution $M\\preceq D$ of density $(1-δ)$ on which $b$ is nearly optimally quantum-hard to predict. - Post-quantum interactive XOR lemma: Given any classically-interactive protocol, if quantum adversaries have advantage at most $δ$ in guessing a private challenger bit $b$, then two sequential repetitions reduce the advantage for predicting the XOR of the challenger bits $b_1\\oplus b_2$ to at most $δ^2+\\rm{negl}(λ)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.05527",
  "author_total": 2,
  "authors": [
    {
      "name": "James Bartusek"
    },
    {
      "name": "Itay Shalit"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2743v2vx2ceay.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.05527",
  "fulltext_url": null,
  "id": "2743v2vx2ceay",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.05527",
  "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.CR"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7163659328",
  "pdf_url": "https://arxiv.org/pdf/2606.05527",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2743v2vx2ceay.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2606.05527",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.05527"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "On the Cryptographic Structure Required for Verifying Qubits",
  "title_text": "On the Cryptographic Structure Required for Verifying Qubits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/2743v2vx2ceay",
  "venue": "arXiv",
  "versions": []
}