{
  "annotation_id": "66444b88-0e57-4ea7-b53a-87d30e74e8af",
  "date_created": "2026-03-02T18:01:42.416000Z",
  "date_modified": "2026-03-02T18:01:42.416000Z",
  "file_hash": "52ce2fddb157b1dab8a00f74c0c3ab7c557d7fffc5063c2aeac5bcb9d2151d01",
  "private": false,
  "record": {
    "abstract": "A remarkable feature of quantum entanglement is that an entangled state of\ntwo parties, Alice (A) and Bob (B), may be more disordered locally than\nglobally. That is, S(A) \u003e S(A,B), where S(.) is the von Neumann entropy. It is\nknown that satisfaction of this inequality implies that a state is\nnon-separable. In this paper we prove the stronger result that for separable\nstates the vector of eigenvalues of the density matrix of system AB is\nmajorized by the vector of eigenvalues of the density matrix of system A alone.\nThis gives a strong sense in which a separable state is more disordered\nglobally than locally and a new necessary condition for separability of\nbipartite states in arbitrary dimensions. We also investigate the extent to\nwhich these conditions are sufficient to characterize separability, exhibiting\nexamples that show separability cannot be characterized solely in terms of the\nlocal and global spectra of a state. We apply our conditions to give a simple\nproof that non-separable states exist sufficiently close to the completely\nmixed state of $n$ qudits.",
    "arxiv_id": "quant-ph/0011117",
    "authors": [
      "M. A. Nielsen",
      "J. Kempe"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevLett.86.5184",
    "journal_ref": "Phys. Rev. Lett., Vol. 86, 5184-7 (2001)",
    "title": "Separable states are more disordered globally than locally",
    "url": "https://arxiv.org/abs/quant-ph/0011117"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e21c4886-5e1a-4b51-8ac4-8e89d4bd833e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}