{
  "abstract": "We characterize the bath resources needed to supply repeated uses of a fixed finite-dimensional quantum channel in a closed device. For each horizon $T$, one bath, one initial state and one repeated unitary are fixed before the user. Each output is returned before the next input arrives; no reset, discard, fresh ancilla or uncounted controller is available. Approximation error must vanish against arbitrary adaptive users with quantum memory and references. Writing $r=\\lim \\log_2(R_T)/T$ for the bath dimension rate and $s=\\lim S(ω_T)/T$ for the actual initial entropy rate, we prove that the achievable region is exactly $s\\ge 0$, $r+s\\ge h$ and $r-s\\geκ$. Here $h$ is maximum entropy exchange and $κ$ is a smoothed independent-reference extension cost, with the zero-error limit taken before the supremum over full-rank inputs. Its exact fixed-input form is an affine transform of the zero-leakage quantum privacy funnel. The minimum dimension rate is $(h+κ)/2$. The proof combines entropy converses, a bath-dimension-independent support repair, and a closed adaptive implementation of encoder-only fully quantum Slepian--Wolf recycling. All seeds, clocks, workspace and retained residues are counted. Worked examples include dephasing, pure replacement and a qubit channel with $0<κ<h$. No computability of $κ$ or efficient circuit synthesis is claimed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18267",
  "author_total": 1,
  "authors": [
    {
      "name": "Seth Douglas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cqfk5awkk78h0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18267",
  "fulltext_url": null,
  "id": "cqfk5awkk78h0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18267",
  "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",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7213505598",
  "pdf_url": "https://arxiv.org/pdf/2609.18267",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cqfk5awkk78h0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.18267",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18267"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Bath dimension and initial entropy for closed repeated use of a quantum channel",
  "title_text": "Bath dimension and initial entropy for closed repeated use of a quantum channel",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/cqfk5awkk78h0",
  "venue": "arXiv",
  "versions": []
}