{
  "abstract": "A finite group-valued temporal reference frame defines a correlated random-unitary process rather than a list of independent channels. We identify a regime in which its complete trajectory law is an exact operational coordinate. If the carrier contains every irreducible representation of the finite group $G$, one ancilla-assisted input resolves all group elements, and for arbitrary laws $μ,ν$ on $G^n$ the strategy half-distance equals $d_{\\mathrm{TV}}(μ,ν)$. Optimal output-side causal post-processing likewise reduces to classical convolution on $G^n$. This converts temporal hiding into a $q$-ary coding problem. Uniform coset laws of an $[n,k]_q$ code are identical on every set of fewer than $d(C^\\perp)$ slots and perfectly distinguishable globally. For $M$ sectors with leakage at most $η$ from $t$ selected slots and global decoding error $ε$, we obtain $(1-ε)\\log M \\leq (n-t)\\log q+η+h_2(ε)$. For nested codes $C\\subset D$, the payload $R=\\dim D-\\dim C$, invisible depth $t=d_{\\mathrm{rel}}(C^\\perp,D^\\perp)-1$, and sector distance $d_{\\mathrm{rel}}(D,C)$ obey $R+t+d_{\\mathrm{rel}}(D,C)-1\\leq n$ and $R+t+2e+f\\leq n$, where $e$ and $f$ are adversarial errors and known erasures. Nested generalized Reed-Solomon codes attain the bounds in their existence range. We also give the exact projection-rank leakage profile and show that hiding arbitrary coherent superpositions from $t$ slots is precisely quantum erasure correction, yielding $\\log_q K+2t\\leq n$. The results separate classical trajectory privacy from coherent temporal privacy and quantify the robust payload hidden from reduced process tomography.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18948",
  "author_total": 1,
  "authors": [
    {
      "name": "Maxim V. Churilov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f3btntr653xhz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18948",
  "fulltext_url": null,
  "id": "f3btntr653xhz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18948",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7213493244",
  "pdf_url": "https://arxiv.org/pdf/2609.18948",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f3btntr653xhz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.18948",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18948"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Optimal Temporal Hiding in Correlated Quantum Reference-Frame Processes",
  "title_text": "Optimal Temporal Hiding in Correlated Quantum Reference-Frame Processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/f3btntr653xhz",
  "venue": "arXiv",
  "versions": []
}