{
  "annotation_id": "e15ff11d-d7e6-4461-80cd-33969f440c22",
  "date_created": "2026-03-02T18:02:33.641000Z",
  "date_modified": "2026-03-02T18:02:33.641000Z",
  "file_hash": "68b67f5d399f202d85ddda2a5cc5d5c5cb0ad834ecb0c4b7110b3bcd2dfd6537",
  "private": false,
  "record": {
    "abstract": "We give improved upper bounds on the radius of the largest ball of separable\nstates of an m-qubit system around the maximally mixed state. The ratio between\nthe upper bound and the best known lower bound (Hildebrand, quant.ph/0601201)\nthus shrinks to a constant c = \\sqrt{34/27} ~ 1.122, as opposed to a term of\norder \\sqrt{m\\log m} for the best upper bound known previously (Aubrun and\nSzarek, quant.ph/0503221). We give concrete examples of separable states on the\nboundary to entanglement which realize these upper bounds. As a by-product, we\ncompute the radii of the largest balls that fit into the projective tensor\nproduct of four unit balls in R^3 and in the projective tensor product of an\narbitrary number of unit balls in R^n for n = 2,4,8.",
    "arxiv_id": "quant-ph/0702040",
    "authors": [
      "Roland Hildebrand"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.75.062330",
    "title": "Entangled states close to the maximally mixed state",
    "url": "https://arxiv.org/abs/quant-ph/0702040"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8877e0f9-60af-4b39-80db-4f3e0c460ed1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}