{
  "annotation_id": "404deb0c-5111-47c0-987f-db1eac1ecbfa",
  "date_created": "2026-03-02T18:02:34.604000Z",
  "date_modified": "2026-03-02T18:02:34.604000Z",
  "file_hash": "329c494c5be900eefb6b45a91dcc6bbe3ef243414507ddeda65010222fa74038",
  "private": false,
  "record": {
    "abstract": "Two kinds of Bell-states diagonal (BSD) entanglement witnesses (EW) are\nconstructed by using the algebra of Dirac $\\gamma$ matrices in the space-time\nof arbitrary dimension $d$, where the first kind can detect some BSD\nrelativistic and non-relativistic $m$-partite multispinor bound entangled\nstates in Hilbert space of dimension $2^{m\\lfloor d/2\\rfloor}$, including the\nbipartite Bell-type and iso-concurrence type states in the four-dimensional\nspace-time ($d=4$). By using the connection between Hilbert-Schmidt measure and\nthe optimal EWs associated with states, it is shown that as far as the spin\nquantum correlations is concerned, the amount of entanglement is not a\nrelativistic scalar and has no invariant meaning. The introduced EWs are\nmanipulated via the linear programming (LP) which can be solved exactly by\nusing simplex method. The decomposability or non-decomposability of these EWs\nis investigated, where the region of non-decomposable EWs of the first kind is\npartially determined and it is shown that, all of the EWs of the second kind\nare decomposable. These EWs have the preference that in the bipartite systems,\nthey can determine the region of separable states, i.e., bipartite\nnon-detectable density matrices of the same type as the EWs of the first kind\nare necessarily separable. Also, multispinor EWs with non-polygon feasible\nregions are provided, where the problem is solved by approximate LP, and in\ncontrary to the exactly manipulatable EWs, both the first and second kind of\nthe optimal approximate EWs can detect some bound entangled states.\n  Keywords: Relativistic entanglement, Entanglement Witness, Multispinor,\nLinear Programming, Feasible Region. PACs Index: 03.65.Ud",
    "arxiv_id": "quant-ph/0703106",
    "authors": [
      "M. A. Jafarizadeh",
      "R. Sufiani"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.77.012105",
    "title": "Bell-states diagonal entanglement witnesses for relativistic and   non-relativistic multispinor systems in arbitrary dimensions",
    "url": "https://arxiv.org/abs/quant-ph/0703106"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bb3375e9-a50c-4429-995b-69272ce533c4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}