{
  "abstract": "A two-level emitter chirally coupled to a waveguide imprints a $π$ conditional phase on a two-photon pulse, a key component assumed in quantum photonic neural network architectures, but whether it survives the pure dephasing of a solid-state emitter is unknown, since no two-photon scattering treatment includes it. We derive the dephased two-photon amplitude in closed form and validate it against an independent Fock-state master equation. The conditional phase is pinned at exactly $π$ at every dephasing rate examined: dephasing destroys the amplitude carrying the nonlinear phase rather than rotating it. The one- and two-photon channels are not attenuated equally, so dephasing does not simply scale the node down but reweights it between photon-number sectors---an error no phase setting can train away. The standard factorization of two-photon correlators, exact for arbitrary loss, fails at first order in $γ_ϕ$, discarding $16$--$81\\%$ of pairs over $γ_ϕ/γ=0.1$--$1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30098",
  "author_total": 2,
  "authors": [
    {
      "name": "Matthew Kozma"
    },
    {
      "name": "Stephen Hughes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/48zpnbmvmpe9g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30098",
  "fulltext_url": null,
  "id": "48zpnbmvmpe9g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30098",
  "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",
      "3107|Quantum optics and atomic interactions"
    ]
  ],
  "openalex": "W7223221093",
  "pdf_url": "https://arxiv.org/pdf/2610.30098",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/48zpnbmvmpe9g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:19Z",
      "native_id": "2610.30098",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30098"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Pure dephasing destroys two-photon amplitude, not nonlinear phase",
  "title_text": "Pure dephasing destroys two-photon amplitude, not nonlinear phase",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:19Z",
  "url": "https://research.draconitic.com/paper/48zpnbmvmpe9g",
  "venue": "arXiv",
  "versions": []
}