{
  "abstract": "Nonlinear properties of quantum states are essential to quantum information and many-body physics, but assessing them experimentally is challenging, as it typically requires multi-copy operations or a large number of measurement settings. To address this challenge, we develop a universal framework, collision-based nonlinear estimation (CBNE), for efficiently measuring nonlinear quantities of a quantum state $ρ$, such as the higher-order expectation value ${\\rm tr}(Oρ^t)$ for some observable $O$, using single-copy randomized measurements. Strikingly, our protocol requires only a single measurement setting, provided that the system dimension is sufficiently large or a few ancillary qubits are available; this contrasts with the conventional expectation that multiple measurement bases are necessary for nonlinear estimation. In addition, CBNE is observable-independent at the experimental stage, which enables simultaneous estimation of multiple nonlinear functions. It further extends to broader tasks, including the estimation of principal component properties and partial-transpose moments of quantum states. Our results provide a practical and scalable route for measuring nonlinear state properties on near-term quantum devices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.09958",
  "author_total": 5,
  "authors": [
    {
      "name": "Zihao Li"
    },
    {
      "name": "Datong Chen"
    },
    {
      "name": "Dayue Qin"
    },
    {
      "name": "Yuxiang Yang"
    },
    {
      "name": "You Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bfa7dv06ent7w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.09958",
  "fulltext_url": null,
  "id": "bfa7dv06ent7w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.09958",
  "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",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7160959427",
  "pdf_url": "https://arxiv.org/pdf/2605.09958",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bfa7dv06ent7w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2605.09958",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.09958"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Nonlinear Properties from a Single Measurement Setting",
  "title_text": "Quantum Nonlinear Properties from a Single Measurement Setting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:48Z",
  "url": "https://research.draconitic.com/paper/bfa7dv06ent7w",
  "venue": "arXiv",
  "versions": []
}