{
  "annotation_id": "b8ace92f-4472-4959-827b-b6dfc4382899",
  "date_created": "2026-03-02T18:02:16.526000Z",
  "date_modified": "2026-03-02T18:02:16.526000Z",
  "file_hash": "86ec9ae1314a3820f9b6eecb654b274905d6f0d1c12b5a9159c8b4c6e8535672",
  "private": false,
  "record": {
    "abstract": "We prove additivity of the minimal conditional entropy associated with a\nquantum channel Phi, represented by a completely positive (CP),\ntrace-preserving map, when the infimum of S(gamma_{12}) - S(gamma_1) is\nrestricted to states of the form gamma_{12} = (I \\ot Phi)(| psi \u003e\u003c psi |). We\nshow that this follows from multiplicativity of the completely bounded norm of\nPhi considered as a map from L_1 -\u003e L_p for L_p spaces defined by the Schatten\np-norm on matrices; we also give an independent proof based on entropy\ninequalities. Several related multiplicativity results are discussed and\nproved. In particular, we show that both the usual L_1 -\u003e L_p norm of a CP map\nand the corresponding completely bounded norm are achieved for positive\nsemi-definite matrices. Physical interpretations are considered, and a new\nproof of strong subadditivity is presented.",
    "arxiv_id": "quant-ph/0506196",
    "authors": [
      "Igor Devetak",
      "Marius Junge",
      "Christopher King",
      "Mary Beth Ruskai"
    ],
    "categories": [
      "quant-ph",
      "math.OA"
    ],
    "doi": "10.1007/s00220-006-0034-0",
    "journal_ref": "Commun. Math. Phys. 266, 37-63 (2006)",
    "title": "Multiplicativity of completely bounded p-norms implies a new additivity   result",
    "url": "https://arxiv.org/abs/quant-ph/0506196"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c0021eae-ce1f-488b-92d8-cb43a50b5568",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}