{
  "abstract": "We study agnostic tomography of pure bosonic Gaussian states: given copies of an arbitrary $n$-mode bosonic state $ρ$, the goal is to output a pure Gaussian state whose infidelity with $ρ$ is at most $\\mathrm{opt} + ε$, where $\\mathrm{opt}$ is the minimum infidelity achievable by any pure Gaussian state. We give efficient protocols achieving this in both the high and low fidelity regimes. When $\\mathrm{opt}$ is below some universal constant, our protocol has runtime and copy complexity which is strongly polynomial in $n, 1/ε$ and $\\log \\log E$, where $E$ is the energy of the closest pure Gaussian state. For arbitrary $\\mathrm{opt}$, our protocol uses $(n+1)^{\\mathrm{poly}(1/ε)} \\mathrm{poly}\\left(1+\\log\\log(E)\\right)$ copies and runtime. As a corollary, we obtain the first truly tolerant Gaussianity testing protocol for distinguishing whether $\\mathrm{opt} > c + ε$ or $\\mathrm{opt} < c - ε$, for any threshold $c\\in(0,1)$. We also prove $\\mathrm{poly}(n,1/ε)$ runtime is impossible, unless $\\mathrm{NP}\\subseteq\\mathrm{BQP}$. Our protocols follow a shared paradigm: first, we iteratively use general Gaussian measurements combined with techniques from classical robust statistics to obtain a good warm start estimate, then we leverage non-Gaussian measurements to refine this warm start using convex and non-convex optimization methods. Interestingly, we prove that non-Gaussian measurements are necessary to match the strong agnostic guarantees we obtain, and in fact these guarantees are provably superior to what is possible for robustly estimating classical Gaussians.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06810",
  "author_total": 5,
  "authors": [
    {
      "name": "Alvan Arulandu"
    },
    {
      "name": "Sitan Chen"
    },
    {
      "name": "Ziyun Chen"
    },
    {
      "name": "Jerry Li"
    },
    {
      "name": "Eric Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8xf0q6m5w5vet.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06810",
  "fulltext_url": null,
  "id": "8xf0q6m5w5vet",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06810",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7220696487",
  "pdf_url": "https://arxiv.org/pdf/2610.06810",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8xf0q6m5w5vet.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:05Z",
      "native_id": "2610.06810",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06810"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Finding Gaussian Structure in Bosonic States",
  "title_text": "Finding Gaussian Structure in Bosonic States",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/8xf0q6m5w5vet",
  "venue": "arXiv",
  "versions": []
}