{
  "annotation_id": "e254d79d-db1f-40e7-905b-ab33a7fa8cb2",
  "date_created": "2026-03-02T18:02:19.887000Z",
  "date_modified": "2026-03-02T18:02:19.887000Z",
  "file_hash": "e499dab889952a074148a5296eae91915cb2dbab8481e2ae62f3e37199a7d089",
  "private": false,
  "record": {
    "abstract": "Recently, Laplacian matrices of graphs are studied as density matrices in\nquantum mechanics. We continue this study and give conditions for separability\nof generalized Laplacian matrices of weighted graphs with unit trace. In\nparticular, we show that the Peres-Horodecki positive partial transpose\nseparability condition is necessary and sufficient for separability in\n${\\mathbb C}^2\\otimes {\\mathbb C}^q$. In addition, we present a sufficient\ncondition for separability of generalized Laplacian matrices and diagonally\ndominant nonnegative matrices.",
    "arxiv_id": "quant-ph/0508163",
    "authors": [
      "Chai Wah Wu"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1016/j.physleta.2005.10.049",
    "journal_ref": "Expanded version in Physics Letters A, 251 (1-2), pp. 18-22, 2006",
    "title": "Conditions for separability in generalized Laplacian matrices and   nonnegative matrices as density matrices",
    "url": "https://arxiv.org/abs/quant-ph/0508163"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "17279662-d208-414a-acfa-bd7ae53f1ff5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}