{
  "abstract": "Quantum networks distribute entanglement between distant nodes by combining many short entangled links using local quantum operations. These operations only succeed probabilistically, yet existing percolation-based theories of entanglement transmission treat them as perfect. We approach the problem through statistical physics, using a stochastic generalization of concurrence percolation to determine how reliable local operations must be for long-range entanglement to remain possible. On hierarchical $(U,V)$-flower networks, which permit full analytical control across network scales, we derive an exact renormalization recursion for the probability that an end-to-end entangled connection survives. For the $(2,2)$-flower this yields a closed-form operational phase boundary, $η_p = 2 - \\frac{32}{27}η_s$, where $η_s$ and $η_p$ are the success probabilities of the series (entanglement swapping) and parallel (purification) operations, respectively. At this boundary the survival probability jumps discontinuously from $0$ to $S_\\infty = 3/(4η_s)$. Numerically propagating the full distribution of end-to-end concurrence yields a second threshold in the initial link quality, which varies continuously with operational reliability. Above both thresholds the large-network state is binary: the connection either fails outright or approaches a perfect Bell pair. Our results thus reveal a two-threshold structure for long-range entanglement, in which operational reliability and initial link quality can compensate one another. Operational success rates therefore emerge alongside initial link quality as a primary design constraint for scalable quantum networks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05069",
  "author_total": 3,
  "authors": [
    {
      "name": "Arn Caesar"
    },
    {
      "name": "Xinqi Hu"
    },
    {
      "name": "Kim Christensen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2atmspfq9kjvy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05069",
  "fulltext_url": null,
  "id": "2atmspfq9kjvy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05069",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05069",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2atmspfq9kjvy.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.05069",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05069"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Operational Thresholds for Long-Range Entanglement in Quantum Networks",
  "title_text": "Operational Thresholds for Long-Range Entanglement in Quantum Networks",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/2atmspfq9kjvy",
  "venue": "arXiv",
  "versions": []
}