{
  "annotation_id": "a1e40fe8-43e6-45e0-8128-c04fe7f2a3f7",
  "date_created": "2026-03-02T18:01:38.148000Z",
  "date_modified": "2026-03-02T18:01:38.148000Z",
  "file_hash": "fea7060ecbf2d222978dcb4d1a21e119e18f0d25fe60cdb308199e16f2602b02",
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  "record": {
    "abstract": "In this paper we develop a mathematical framework for the characterisation of\nseparability and entanglement of formation (EoF) of general bipartite states.\nThese characterisations are of the variational kind, meaning that separability\nand EoF are given in terms of a function which is to be minimized over the\nmanifold of unitary matrices. A major benefit of such a characterisation is\nthat it directly leads to a numerical procedure for calculating EoF. We present\nan efficient minimisation algorithm and an apply it to the bound entangled 3X3\nHorodecki states; we show that their EoF is very low and that their distance to\nthe set of separable states is also very low. Within the same variational\nframework we rephrase the results by Wootters (W. Wootters, Phys. Rev. Lett.\n80, 2245 (1998)) on EoF for 2X2 states and present progress in generalising\nthese results to higher dimensional systems.",
    "arxiv_id": "quant-ph/0006128",
    "authors": [
      "K. Audenaert",
      "F. Verstraete",
      "B. De Moor"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.64.052304",
    "journal_ref": "Phys. Rev. A 64, 052304 (2001)",
    "title": "Variational Characterisations of Separability and Entanglement of   Formation",
    "url": "https://arxiv.org/abs/quant-ph/0006128"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "328202c1-532c-4689-abfe-b81994bd82e2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}