{
  "annotation_id": "ce05d829-66e6-4e4a-809a-fb58cd11e141",
  "date_created": "2026-03-02T18:01:38.729000Z",
  "date_modified": "2026-03-02T18:01:38.729000Z",
  "file_hash": "b6997caf0b85a861255059e5404da4d99c6b753f39d6a9f6a666ab71ad4fe37e",
  "private": false,
  "record": {
    "abstract": "An entanglement witness (EW) is an operator that allows to detect entangled\nstates. We give necessary and sufficient conditions for such operators to be\noptimal, i.e. to detect entangled states in an optimal way. We show how to\noptimize general EW, and then we particularize our results to the\nnon-decomposable ones; the latter are those that can detect positive partial\ntranspose entangled states (PPTES). We also present a method to systematically\nconstruct and optimize this last class of operators based on the existence of\n``edge\u0027\u0027 PPTES, i.e. states that violate the range separability criterion\n[Phys. Lett. A{\\bf 232}, 333 (1997)] in an extreme manner. This method also\npermits the systematic construction of non-decomposable positive maps (PM). Our\nresults lead to a novel sufficient condition for entanglement in terms of\nnon-decomposable EW and PM. Finally, we illustrate our results by constructing\noptimal EW acting on $H=\\C^2\\otimes \\C^4$. The corresponding PM constitute the\nfirst examples of PM with minimal ``qubit\u0027\u0027 domain, or - equivalently - minimal\nhermitian conjugate codomain.",
    "arxiv_id": "quant-ph/0005014",
    "authors": [
      "M. Lewenstein",
      "B. Kraus",
      "J. I. Cirac",
      "P. Horodecki"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.62.052310",
    "title": "Optimization of entanglement witnesses",
    "url": "https://arxiv.org/abs/quant-ph/0005014"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c8461914-0bd5-4e66-975c-671118dc839d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}