{
  "annotation_id": "936238fb-efdc-45f7-a629-ec2c6527c7e9",
  "date_created": "2026-03-02T18:02:10.295000Z",
  "date_modified": "2026-03-02T18:02:10.295000Z",
  "file_hash": "c2670bd3127d56617eeacc230f4aaa69a7a86e2efd6417a1e0f869c61b88c19a",
  "private": false,
  "record": {
    "abstract": "We investigate several problems in entanglement theory from the perspective\nof convex optimization. This list of problems comprises (A) the decision\nwhether a state is multi-party entangled, (B) the minimization of expectation\nvalues of entanglement witnesses with respect to pure product states, (C) the\nclosely related evaluation of the geometric measure of entanglement to quantify\npure multi-party entanglement, (D) the test whether states are multi-party\nentangled on the basis of witnesses based on second moments and on the basis of\nlinear entropic criteria, and (E) the evaluation of instances of maximal output\npurities of quantum channels. We show that these problems can be formulated as\ncertain optimization problems: as polynomially constrained problems employing\npolynomials of degree three or less. We then apply very recently established\nknown methods from the theory of semi-definite relaxations to the formulated\noptimization problems. By this construction we arrive at a hierarchy of\nefficiently solvable approximations to the solution, approximating the exact\nsolution as closely as desired, in a way that is asymptotically complete. For\nexample, this results in a hierarchy of novel, efficiently decidable sufficient\ncriteria for multi-particle entanglement, such that every entangled state will\nnecessarily be detected in some step of the hierarchy. Finally, we present\nnumerical examples to demonstrate the practical accessibility of this approach.",
    "arxiv_id": "quant-ph/0407135",
    "authors": [
      "J. Eisert",
      "P. Hyllus",
      "O. Guehne",
      "M. Curty"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.other",
      "math.OC"
    ],
    "doi": "10.1103/PhysRevA.70.062317",
    "journal_ref": "Phys. Rev. A 70, 062317 (2004)",
    "title": "Complete hierarchies of efficient approximations to problems in   entanglement theory",
    "url": "https://arxiv.org/abs/quant-ph/0407135"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9cdc9be8-41fb-47cc-8e11-b3734eab145b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}