{
  "abstract": "Nonlinear exceptional points (NEPs) were proposed to circumvent the noise--responsivity cancellation that limits linear exceptional-point sensors. At an NEP, the stationary frequency response can be singular while the Hamiltonian Petermann factor remains finite, suggesting a genuine signal-to-noise ratio (SNR) enhancement. Yet recent model-specific analyses of nonlinear fluctuations have reached conflicting conclusions. We prove that any singular stationary frequency response requires a fixed-point bifurcation of the nonlinear dynamics. In local fluctuation regimes, the singularities in responsivity and long-time frequency uncertainty are both set by the critical relaxation rate, leading to exact cancellation in the SNR and precluding any divergent enhancement. Furthermore, we derive a path-information bound that applies across both local and nonlinear fluctuation regimes and places a finite ceiling on the long-time SNR enhancement. Notably, this upper bound is attainable in the local fluctuation regime, implying that frequency readout under such parameter settings is information-optimal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39046",
  "author_total": 2,
  "authors": [
    {
      "name": "Xue-Hao Yu"
    },
    {
      "name": "Cong-Feng Qiao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dv1gsbh523hxy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39046",
  "fulltext_url": null,
  "id": "dv1gsbh523hxy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39046",
  "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",
      "physics.optics"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Non-Hermitian Physics"
    ]
  ],
  "openalex": "W7215058567",
  "pdf_url": "https://arxiv.org/pdf/2609.39046",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dv1gsbh523hxy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39046",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39046"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Fixed-Point Bifurcations and Path-Information Bounds in Nonlinear Exceptional-Point Sensing",
  "title_text": "Fixed-Point Bifurcations and Path-Information Bounds in Nonlinear Exceptional-Point Sensing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/dv1gsbh523hxy",
  "venue": "arXiv",
  "versions": []
}