{
  "annotation_id": "1a98d7ba-0011-4a50-9a87-059b1d0903f1",
  "date_created": "2026-03-02T18:02:23.615000Z",
  "date_modified": "2026-03-02T18:02:23.615000Z",
  "file_hash": "cf5a62988613d29f61baeef9e6547dfcab634199105740770a80af1526b1e30a",
  "private": false,
  "record": {
    "abstract": "In this paper we give a method to associate a graph with an arbitrary density\nmatrix referred to a standard orthonormal basis in the Hilbert space of a\nfinite dimensional quantum system. We study the related issues like\nclassification of pure and mixed states, Von-Neumann entropy, separability of\nmultipartite quantum states and quantum operations in terms of the graphs\nassociated with quantum states. In order to address the separability and\nentanglement questions using graphs, we introduce a modified tensor product of\nweighted graphs, and establish its algebraic properties. In particular, we show\nthat Werner\u0027s definition [1] of a separable state can be written in terms of a\ngraphs, for the states in a real or complex Hilbert space. We generalize the\nseparability criterion (degree criterion) due to S.L. Braunstein, S. Ghosh, T.\nMansour, S. Severini, R.C. Wilson [2], to a class of weighted graphs with real\nweights. We have given some criteria for the Laplacian associated with a\nweighted graph to be positive semidefinite.",
    "arxiv_id": "quant-ph/0602053",
    "authors": [
      "Ali Saif M. Hassan",
      "Pramod Joag"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/1751-8113/40/33/019",
    "journal_ref": "J. Phys. A: Math. Theor. 40 (2007) 10251--10290",
    "title": "Combinatorial approach to multipartite quantum systems:basic formulation",
    "url": "https://arxiv.org/abs/quant-ph/0602053"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "90ab85f5-49de-4a6d-bd40-e4e1d8261103",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}