{
  "annotation_id": "e4eb6714-bbfd-4488-945d-54494a71ecc3",
  "date_created": "2026-03-02T18:01:39.318000Z",
  "date_modified": "2026-03-02T18:01:39.318000Z",
  "file_hash": "598c6c4a54c91c91aaac33589fe95f9f538ea5ab811cd6db484cb36242bd6e9f",
  "private": false,
  "record": {
    "abstract": "Every entangled state can be perturbed, for instance by decoherence, and stay\nentangled. For a large class of pure entangled states, we show how large the\nperturbation can be. Our class includes all pure bipartite and all maximally\nentangled states. For an entangled state, E, the constucted neighborhood of\nentangled states is the region outside two parallel hyperplanes, which sandwich\nthe set of all separable states. The states for which these neighborhoods are\nlargest are the maximally entangled ones. As the number of particles, or the\ndimensions of the Hilbert spaces for two of the particles increases, the\ndistance between two of the hyperplanes which sandwich the separable states\ngoes to zero. It is easy to decide if a state Q is in the neighborhood of\nentangled states we construct for an entangled state E. One merely has to check\nif the trace of EQ is greater than a constant which depends upon E and which we\ndetermine.",
    "arxiv_id": "quant-ph/0009090",
    "authors": [
      "Robert Lockhart",
      "Michael Steiner"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.65.022107",
    "title": "Preserving entanglement under decoherence and sandwiching all separable   states",
    "url": "https://arxiv.org/abs/quant-ph/0009090"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0f29c66e-9597-4ced-bf82-40eae13ad8a1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}