{
  "annotation_id": "0851185b-18d7-4781-8537-f6dec56273c8",
  "date_created": "2026-03-02T18:02:48.580000Z",
  "date_modified": "2026-03-02T18:02:48.580000Z",
  "file_hash": "0209e807eb54309ba5d1734b33a709cd819c693b270e5544b6d985876f0e1dc4",
  "private": false,
  "record": {
    "abstract": "We introduce the notion of a Schmidt number of a bipartite density matrix,\ncharacterizing the minimum Schmidt rank of the pure states that are needed to\nconstruct the density matrix. We prove that Schmidt number is nonincreasing\nunder local quantum operations and classical communication. We show that\n$k$-positive maps witness Schmidt number, in the same way that positive maps\nwitness entanglement. We show that the family of states which is made from\nmixing the completely mixed state and a maximally entangled state have\nincreasing Schmidt number depending on the amount of maximally entangled state\nthat is mixed in. We show that Schmidt number {\\it does not necessarily\nincrease} when taking tensor copies of a density matrix $\\rho$; we give an\nexample of a density matrix for which the Schmidt numbers of $\\rho$ and $\\rho\n\\otimes \\rho$ are both 2.",
    "arxiv_id": "quant-ph/9911117",
    "authors": [
      "Barbara M. Terhal",
      "Pawel Horodecki"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.61.040301",
    "journal_ref": "Phys. Rev. A Rapid Communications Vol.61,040301 (2000)",
    "title": "A Schmidt number for density matrices",
    "url": "https://arxiv.org/abs/quant-ph/9911117"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5c691f51-b9a3-4b7f-84a1-126edb44f1b8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}