{
  "abstract": "Quantum experiments without a definite causal order offer new ways to distinguish devices, estimate physical parameters, and communicate. We prove a common limit on these tasks: the geometric Rényi divergence at the output of a deterministic completely positive process cannot exceed the sum of the divergences of its individual channel uses. The inequality holds for every Rényi order in $(0,1)\\cup(1,2]$ and any number of independently replaceable channels. Parallel experiments with separate reference-assisted inputs approach the bound, giving an exact equality after optimization over processes. We also prove an additive bound on the right logarithmic derivative Fisher information of parameter-dependent channels under every fixed process in this class. A resulting Cramér--Rao bound limits locally unbiased estimation precision without assuming a definite causal order, and an erasure-probability example attains the bound. The proofs for the geometric Rényi divergence and RLD Fisher information follow from the requirement that every independent choice of channels produce a normalized output. We show how this requirement controls positive local operations, and how small channel perturbations convert the divergence inequality into a Fisher-information bound, including for singular channels. Further applications give finite-use bounds on channel discrimination and exclusion, together with communication and private-state-generation converses when the processes preserve the relevant comparison conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39217",
  "author_total": 2,
  "authors": [
    {
      "name": "Zixin Huang"
    },
    {
      "name": "Mark M. Wilde"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4pzj9hsen04b8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39217",
  "fulltext_url": null,
  "id": "4pzj9hsen04b8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39217",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39217",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4pzj9hsen04b8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.39217",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39217"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Geometric Rényi divergence and RLD Fisher information under quantum processes without definite causal order",
  "title_text": "Geometric Rényi divergence and RLD Fisher information under quantum processes without definite causal order",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:45Z",
  "url": "https://research.draconitic.com/paper/4pzj9hsen04b8",
  "venue": "arXiv",
  "versions": []
}