{
  "abstract": "We study a multilinear optimization problem for tensors with bounded Frobenius norm, where each of the $k$ local factors of dimension $d$ is chosen from a convex set. We give a deterministic algorithm running in time $d^{O(k)}$ for constant additive approximations. As applications, we obtain the first polynomial-time algorithms at constant accuracy for weak membership in the nuclear-norm unit ball of high-order tensors and for multipartite quantum separability in Frobenius norm. Our approach views tensor optimization as a cooperative multiprover game and combines this perspective with a recursive spectral compression procedure. We then show that related ideas admit a quantum implementation when the input state is given through copies, rather than an explicit classical description. In these settings we obtain an algorithm to solve Frobenius-norm separability testing using $\\text{poly}(k)$ copies and $\\text{poly}(k\\log d)$ time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03637",
  "author_total": 2,
  "authors": [
    {
      "name": "Martino Bernasconi"
    },
    {
      "name": "Giulio Malavolta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/at915w712856d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03637",
  "fulltext_url": null,
  "id": "at915w712856d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03637",
  "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 Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220379132",
  "pdf_url": "https://arxiv.org/pdf/2610.03637",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/at915w712856d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03637",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03637"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Polynomial-Time Algorithms for Nuclear Tensor Norms and Multipartite Separability",
  "title_text": "Polynomial-Time Algorithms for Nuclear Tensor Norms and Multipartite Separability",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:18Z",
  "url": "https://research.draconitic.com/paper/at915w712856d",
  "venue": "arXiv",
  "versions": []
}