{
  "abstract": "The $f$-routing protocol is a leading candidate for quantum position verification (Kent, Munro, and Spiller, 2011), but security guarantees for explicit functions remain limited. We prove unconditional resource lower bounds for uniform attackers; our new techniques bypass communication-complexity bounds central to previous works, which are inherently at most linear in the input length. We show that, for input length $n$ and sufficiently small constant $ε>0$, a uniformly generated strategy using $q$ qubits and having description length $\\mathrm{poly}(q)$, with success probability at least $1-ε$ on every input, implies the following computational bounds on $f$: 1. If the strategies are arbitrary quantum channels, then $f\\in\\mathrm{QSZK}(\\mathrm{poly}(nq))$, where $\\mathrm{QSZK}(T)$ is the class of languages having quantum statistical zero knowledge proofs in which the verifier runs in time $T$ (and the simulator in time $\\mathrm{poly}(T)$). 2. If the strategies are explicit Pauli-sparse unitaries on $q$ qubits that have at most $s$ nonzero Pauli coefficients, then $f\\in\\mathrm{DTIME}(\\mathrm{poly}(nqs))$. 3. If the strategies are Clifford+T circuits using at most $t$ magic gates, then $f\\in\\mathrm{DTIME}(\\mathrm{poly}(nq2^t))$. Time and space hierarchies then yield explicit functions secure against polynomial and even quasipolynomial qubits $q$ under our computational restrictions. These bounds exceed the $q\\le\\log n$ bound of Bluhm, Christandl, and Speelman (2022) for inner product function $f=\\mathrm{IP}$, at the cost of restricting adversarial computation and increasing honest evaluation complexity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40278",
  "author_total": 2,
  "authors": [
    {
      "name": "Oren Renard"
    },
    {
      "name": "Nicholas Spooner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/558n8mv1416hd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40278",
  "fulltext_url": null,
  "id": "558n8mv1416hd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40278",
  "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 Information and Cryptography"
    ]
  ],
  "openalex": "W7215117666",
  "pdf_url": "https://arxiv.org/pdf/2609.40278",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/558n8mv1416hd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40278",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40278"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Computational Bounds for $f$-Routing",
  "title_text": "Computational Bounds for f-Routing",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/558n8mv1416hd",
  "venue": "arXiv",
  "versions": []
}