{
  "annotation_id": "22a1c852-a0e6-439b-a0ea-8efb87e499ce",
  "date_created": "2026-03-02T18:02:41.610000Z",
  "date_modified": "2026-03-02T18:02:41.610000Z",
  "file_hash": "ba55e4b699c28b00c1ec7016240aedcc166d75869c129c5845c547cb88b3020a",
  "private": false,
  "record": {
    "abstract": "As far as entanglement is concerned, two density matrices of $n$ particles\nare equivalent if they are on the same orbit of the group of local unitary\ntransformations, $U(d_1)\\times...\\times U(d_n)$ (where the Hilbert space of\nparticle $r$ has dimension $d_r$). We show that for $n$ greater than or equal\nto two, the number of independent parameters needed to specify an $n$-particle\ndensity matrix up to equivalence is $\\Pi_r d_r^2 - \\sum_r d_r^2 + n - 1$. For\n$n$ spin-${1\\over 2}$ particles we also show how to characterise generic\norbits, both by giving an explicit parametrisation of the orbits and by finding\na finite set of polynomial invariants which separate the orbits.",
    "arxiv_id": "quant-ph/9801076",
    "authors": [
      "N. Linden",
      "S. Popescu",
      "A. Sudbery"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevLett.83.243",
    "journal_ref": "Phys.Rev.Lett.83:243-247,1999",
    "title": "Non-local properties of multi-particle density matrices",
    "url": "https://arxiv.org/abs/quant-ph/9801076"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b16bbe7f-19cc-4728-9722-e034a8c47a22",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}