{
  "annotation_id": "2fee7d26-7760-4687-b16f-f7e7c06be145",
  "date_created": "2026-03-02T18:01:38.664000Z",
  "date_modified": "2026-03-02T18:01:38.664000Z",
  "file_hash": "562ba88c8462455252daf0d87c50910dce4318f9f39aa2b77a825a84d1dfc017",
  "private": false,
  "record": {
    "abstract": "In this article we propose a quantum version of Shannon\u0027s conditional\nentropy. Given two density matrices $\\rho$ and $\\sigma$ on a finite dimensional\nHilbert space and with $S(\\rho)=-\\tr\\rho\\ln\\rho$ being the usual von Neumann\nentropy, this quantity $S(\\rho|\\sigma)$ is concave in $\\rho$ and satisfies\n$0\\le S(\\rho|\\sigma)\\le S(\\rho)$, a quantum analogue of Shannon\u0027s famous\ninequality. Thus we view $S(\\rho|\\sigma)$ as the entropy of $\\rho$ conditioned\nby $\\sigma$.",
    "arxiv_id": "quant-ph/0003048",
    "authors": [
      "Robert Schrader"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1002/1521-3978(200008)48:8\u003c747::AID-PROP747\u003e3.0.CO;2-T",
    "title": "On a quantum version of Shannon\u0027s conditional entropy",
    "url": "https://arxiv.org/abs/quant-ph/0003048"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "98e2a994-1cdc-4911-a2e2-53b901d59c27",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}