[
    {
        "id": "osp-16998",
        "type": "article-journal",
        "title": "Finding Gaussian Structure in Bosonic States",
        "author": [
            {
                "family": "Arulandu",
                "given": "Alvan"
            },
            {
                "family": "Chen",
                "given": "Sitan"
            },
            {
                "family": "Chen",
                "given": "Ziyun"
            },
            {
                "family": "Li",
                "given": "Jerry"
            },
            {
                "family": "Ma",
                "given": "Eric"
            }
        ],
        "URL": "https://omanscience.com/ar/articles/finding-gaussian-structure-in-bosonic-states",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "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."
    }
]