{
  "annotation_id": "20ba3d24-61e0-49ab-aef0-243c5962ca00",
  "date_created": "2026-03-02T18:02:34.183000Z",
  "date_modified": "2026-03-02T18:02:34.183000Z",
  "file_hash": "c7813042cf7e92526d2d0a75f8bc9505af5773e0d633ecd5a5d70708bf3d7f34",
  "private": false,
  "record": {
    "abstract": "Let L_n be the n-dimensional Lorentz cone. A linear map M from R^m to R^n is\ncalled Lorentz-positive if M[L_m] is contained in L_n. We extend the notion of\nconcurrence, which was initially introduced to quantify the entanglement of\nbipartite density matrices, to Lorentz-positive maps and provide an explicite\nformula for it. This allows us to obtain formulae for the concurrence of\narbitrary positive operators taking 2 x 2 complex hermitian matrices as input\nand consequently of arbitrary bipartite density matrices of rank 2. Namely, let\nP: H(2) \\to H(d) be a positive operator, and let \\lambda_1,...,\\lambda_4 be the\ngeneralized eigenvalues of the pencil \\sigma_2(P(X)) - \\lambda det X, in\ndecreasing order, where \\sigma_2 is the second symmetric function of the\nspectrum. Then the concurrence is given by the expression C(P;X) =\n2\\sqrt{\\sigma_2(P(X)) - \\lambda_2 det X}. As an application, we compute the\nconcurrences of the density matrices of all graphs with 2 edges. Similar\nresults apply for a function which we call I-fidelity, with the second largest\ngeneralized eigenvalue \\lambda_2 replaced by the smallest eigenvalue \\lambda_4.",
    "arxiv_id": "quant-ph/0612064",
    "authors": [
      "Roland Hildebrand"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Concurrence of Lorentz-positive maps",
    "url": "https://arxiv.org/abs/quant-ph/0612064"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e95f0265-2348-468d-9747-71b1a86b57d0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}