{
  "abstract": "Quantum computation gives rise to new pseudorandom primitives for states and unitaries, including pseudorandom state generators (PRSGs), pseudorandom function-like state generators (PRFSGs), and pseudorandom unitaries (PRUs). In this paper, we show a full unitary oracle separation between PRFSGs and PRUs. The separation holds between the strongest state notion and the weakest unitary notion: even adaptively secure, quantum-accessible PRFSGs do not imply non-adaptively secure, forward-only PRUs, even when their implementations are allowed to be non-unitary and use an arbitrary number of ancillary qubits. This reveals a fundamental distinction between pseudorandomness for quantum states and for quantum unitaries. Our main technical idea is to view a candidate PRU construction with access to state generation oracles as a map from the underlying oracle states to implemented unitaries, and to study the derivatives of this map. These derivatives are inherently low rank, and we exploit this low-rank structure to distinguish the resulting unitaries from truly random ones. We believe this differential perspective may be useful for studying other structural questions about quantum states and unitaries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14626",
  "author_total": 1,
  "authors": [
    {
      "name": "Minki Hhan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ccw18v63r9g6y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14626",
  "fulltext_url": null,
  "id": "ccw18v63r9g6y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14626",
  "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": "W7213274743",
  "pdf_url": "https://arxiv.org/pdf/2609.14626",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ccw18v63r9g6y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14626",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14626"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Derivatives of Quantum Randomness: Separating Pseudorandom Unitaries from Pseudorandom (Function-like) States",
  "title_text": "Derivatives of Quantum Randomness: Separating Pseudorandom Unitaries from Pseudorandom (Function-like) States",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/ccw18v63r9g6y",
  "venue": "arXiv",
  "versions": []
}