{
  "abstract": "We introduce a highly general method to determine the energy minimum of spin Hamiltonians over separable states when the single-particle reduced density matrices are fixed. We present efficient numerical methods that reduce the problem to calculations in a two-particle system. For a broad class of very general spin models, we present analytic formulas for the minimum. For ferromagnetic Ising and Ising-like models of spin-j particles, the minimum over separable states on two-colorable lattices, and over symmetric separable states on fully connected graphs, is given by a compact analytic formula involving the quantum Fisher information. For antiferromagnetic Ising-like and XY-like models of spin j-particles living on a complete graph, the energy minimum for symmetric separable states is given with the expectation value of single-particle operators. For the ferromagnetic Heisenberg chain of spin-1/2 particles, the minimum is expressed via the Uhlmann-Jozsa fidelity. These relations enable the extraction of the quantum Fisher information and quantum fidelity of the corresponding single-particle reduced states from correlation measurements on ground-state ensembles of suitably engineered spin models. For a number of other models, we obtain not necessarily tight lower bounds. We also present bounds for various levels of multiparticle entanglement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.03022",
  "author_total": 2,
  "authors": [
    {
      "name": "Géza Tóth"
    },
    {
      "name": "József Pitrik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cjt8a3sp9c9k8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.03022",
  "fulltext_url": null,
  "id": "cjt8a3sp9c9k8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.03022",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7160424627",
  "pdf_url": "https://arxiv.org/pdf/2605.03022",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cjt8a3sp9c9k8.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2605.03022",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.03022"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "General method for obtaining the energy minimum of spin Hamiltonians for separable states",
  "title_text": "General method for obtaining the energy minimum of spin Hamiltonians for separable states",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:21Z",
  "url": "https://research.draconitic.com/paper/cjt8a3sp9c9k8",
  "venue": "arXiv",
  "versions": []
}