{
  "annotation_id": "dfdc6924-c1d2-4944-ba50-483afca6135d",
  "date_created": "2026-03-02T18:01:45.397000Z",
  "date_modified": "2026-03-02T18:01:45.397000Z",
  "file_hash": "d30e5cc1f76aa57f198f45927345b83c846fadc020c8e86207356fec283822c6",
  "private": false,
  "record": {
    "abstract": "From the consideration of measuring bipartite mixed states by separable pure\nstates, we introduce algebraic sets in complex projective spaces for bipartite\nmixed states as the degenerating locus of the measurement. These algebraic sets\nare independent of the eigenvalues and only measure the \"position\" of\neigenvectors of bipartite mixed states. They are nonlocal invariants ie.,\nremaining invariant after local unitary transformations. The algebraic sets\nhave to be the sum of the linear subspaces if the mixed states are separable,\nand thus we give a \"eigenvalue-free\" criterion of separability.Based on our\ncriterion, examples are given to illustrate that entangled mixed states which\nare invariant under partial transposition or fufill entropy and disorder\ncriterion of separability can be constructed systematically.We reveal that a\nlarge part of quantum entanglement is independent of eigenvalue spectra and\ndevelop a method to measure this part of quantum enatnglement.The results are\nextended to multipartite case.",
    "arxiv_id": "quant-ph/0108093",
    "authors": [
      "Hao Chen"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum entanglement without eigenvalue spectra",
    "url": "https://arxiv.org/abs/quant-ph/0108093"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7bec24b9-8c07-41eb-a5e5-ae62445b3de7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}