{
  "annotation_id": "bf9d311f-4e70-455f-b26d-1988320d170a",
  "date_created": "2026-03-02T18:01:46.023000Z",
  "date_modified": "2026-03-02T18:01:46.023000Z",
  "file_hash": "9c744823ef2b87144d9ef0b4db228fbd965eecb22130d06db290a5f8c5ab7a75",
  "private": false,
  "record": {
    "abstract": "All mixed states of two qubits can be brought into normal form by the action\nof SLOCC operations of the kind $\\rho\u0027=(A\\otimes B)\\rho(A\\otimes B)^\\dagger$.\nThese normal forms can be obtained by considering a Lorentz singular value\ndecomposition on a real parameterization of the density matrix. We show that\nthe Lorentz singular values are variationally defined and give rise to\nentanglement monotones, with as a special case the concurrence. Next a\nnecessary and sufficient criterion is conjectured for a mixed state to be\nconvertible into another specific one with a non-zero probability. Finally the\nformalism of the Lorentz singular value decomposition is applied to tripartite\npure states of qubits. New proofs are given for the existence of the GHZ- and\nW-class of states, and a rigorous proof for the optimal distillation of a\nGHZ-state is derived.",
    "arxiv_id": "quant-ph/0108043",
    "authors": [
      "Frank Verstraete",
      "Jeroen Dehaene",
      "Bart De Moor"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.65.032308",
    "journal_ref": "Phys. Rev. A (\\bf 65), 032308 (2002).",
    "title": "The Lorentz singular value decomposition and its applications to pure   states of 3 qubits",
    "url": "https://arxiv.org/abs/quant-ph/0108043"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "dd242b8c-7982-4acc-816c-915ec5541eaf",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}