{
  "abstract": "We initiate the time-bounded meta-complexity program for quantum cryptography. Recent work characterizes one-way puzzles, the minimal search primitive of quantum cryptography without one-way functions, by the average-case hardness of approximating the plain, uncomputable Kolmogorov complexity over quantumly samplable distributions; the classical program of Liu and Pass, by contrast, lives at polynomial time bounds. We define a probabilistic time-bounded quantum program complexity pKq^t for classical strings and prove two unconditional theorems. First, a quantum coding theorem: any string output by a quantum polynomial-time sampler with probability delta admits a description of the information-theoretically optimal length log(1/delta) plus logarithmic terms, decodable by a quantum machine in time O(sqrt(1/delta)) times a polynomial, via amplitude amplification over the coherently executed sampler. Second, an exact characterization at subexponential time: one-way puzzles exist if and only if the gap problem for pKq at time bound 2^(n/2) poly(n) is weakly quantum-average-hard, refining the plain-complexity characterizations. We then isolate the polynomial-time coding theorem as the single load-bearing open conjecture of the program, prove that it implies the full polynomial-time characterization, analyze why the classical derandomization proof resists quantization, and formulate a relativized barrier conjecture delimiting string-valued meta-complexity at one-way puzzles. Conjectures are labeled as such throughout.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02687",
  "author_total": 1,
  "authors": [
    {
      "name": "Morteza Saberikamarposhti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1bje5c9zjrbne.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02687",
  "fulltext_url": null,
  "id": "1bje5c9zjrbne",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02687",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1703|Computability, Logic, AI Algorithms"
    ]
  ],
  "openalex": "W7207626530",
  "pdf_url": "https://arxiv.org/pdf/2609.02687",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1bje5c9zjrbne.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.02687",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02687"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Meta-Complexity Is All You Need: Characterizing One-Way Puzzles via Time-Bounded Kolmogorov Complexity",
  "title_text": "Quantum Meta-Complexity Is All You Need: Characterizing One-Way Puzzles via Time-Bounded Kolmogorov Complexity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:16Z",
  "url": "https://research.draconitic.com/paper/1bje5c9zjrbne",
  "venue": "arXiv",
  "versions": []
}