{
  "abstract": "A paradigmatic task in quantum metrology is that of phase estimation. For this task it is commonly believed, under reasonable assumptions about prior information, that a quadratic advantage in sensitivity is the maximum possible advantage offered by the use of quantum resources. In this work, we consider a channel that implements a phase shift by an angle $2πk/M$, where $k$ is a uniformly random unknown integer, in addition to a small unknown phase shift of interest. We show that, subject to a constraint on the mean photon number per channel use, there is a super-exponential separation between the quantum Fisher information (QFI) attainable using a squeezed vacuum state and that attainable using coherent states. This advantage holds over any state obtained from a coherent state via phase covariant channels. Specifically, when the mean photon number per channel use is 1, the ratio of their QFI grows as $Ω[(M/\\sqrt{2}e)^M]$. For a mean photon number per channel use of $M/\\log(M)$, the squeezed vacuum QFI is $Ω(M^{3/2}/\\sqrt{\\log(M)})$, whereas for a coherent state it is at most $\\exp[-M\\log\\log(M)+O(M)]$. We complement this QFI analysis with non-asymptotic estimation results. For a mean photon number per channel use of $M/\\log M$, an explicit squeezed-vacuum protocol estimates the phase to accuracy $O(1/M)$ using $O(\\sqrt{M\\log M})$ channel uses, whereas every coherent state protocol requires at least $\\exp[M\\log\\log M-O(M)]$ channel uses. We consider the effects of noise and show that the ratio of their QFIs can still grow super-exponentially in $M$. Finally, under fixed optical loss and thermal noise, choosing $\\bar n=M^2/(\\log M)^{3/2}$ allows squeezed vacuum with heterodyne detection to achieve accuracy $O(1/M)$ using sub-polynomially many channel uses, whereas every protocol in the specified classical family requires super-polynomially many.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03657",
  "author_total": 10,
  "authors": [
    {
      "name": "Lorcan O. Conlon"
    },
    {
      "name": "V Vijendran"
    },
    {
      "name": "Aritra Das"
    },
    {
      "name": "Yu-Xin Wang"
    },
    {
      "name": "Erfan Abbasgholinejad"
    },
    {
      "name": "Anthony J. Brady"
    },
    {
      "name": "Jacob Bringewatt"
    },
    {
      "name": "Sean R. Muleady"
    },
    {
      "name": "Syed M. Assad"
    },
    {
      "name": "Alexey V. Gorshkov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0g1gt5pzfrtrd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03657",
  "fulltext_url": null,
  "id": "0g1gt5pzfrtrd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03657",
  "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",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7220416556",
  "pdf_url": "https://arxiv.org/pdf/2610.03657",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0g1gt5pzfrtrd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03657",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03657"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Super-Exponential Advantage of Squeezed Light in Phase Estimation under Discrete Phase Randomisation",
  "title_text": "Super-Exponential Advantage of Squeezed Light in Phase Estimation under Discrete Phase Randomisation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/0g1gt5pzfrtrd",
  "venue": "arXiv",
  "versions": []
}