{
  "annotation_id": "336cce2e-630f-4ccf-8a64-1758da038605",
  "date_created": "2026-03-02T18:02:20.658000Z",
  "date_modified": "2026-03-02T18:02:20.658000Z",
  "file_hash": "9e84a18d7a8c3056cef17a0810eb1844c8e94480bae05222449314d83bfabf82",
  "private": false,
  "record": {
    "abstract": "We propose a general method for introducing extensive characteristics of\nquantum entanglement. The method relies on polynomials of nilpotent raising\noperators that create entangled states acting on a reference vacuum state. By\nintroducing the notion of tanglemeter, the logarithm of the state vector\nrepresented in a special canonical form and expressed via polynomials of\nnilpotent variables, we show how this description provides a simple criterion\nfor entanglement as well as a universal method for constructing the invariants\ncharacterizing entanglement. We compare the existing measures and classes of\nentanglement with those emerging from our approach. We derive the equation of\nmotion for the tanglemeter and, in representative examples of up to four-qubit\nsystems, show how the known classes appear in a natural way within our\nframework. We extend our approach to qutrits and higher-dimensional systems,\nand make contact with the recently introduced idea of generalized entanglement.\nPossible future developments and applications of the method are discussed.",
    "arxiv_id": "quant-ph/0508234",
    "authors": [
      "A. Mandilara",
      "V. M. Akulin",
      "A. V. Smilga",
      "L. Viola"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.74.002331",
    "journal_ref": "Phys.Rev.A74:002331,2006",
    "title": "Description of Quantum Entanglement with Nilpotent Polynomials",
    "url": "https://arxiv.org/abs/quant-ph/0508234"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "05f91c38-0c9d-4ff8-bd01-b5735bfa34dc",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}