{
  "annotation_id": "fcd4c029-f234-4e56-b49b-6afdaccfeda2",
  "date_created": "2026-03-02T18:02:12.909000Z",
  "date_modified": "2026-03-02T18:02:12.909000Z",
  "file_hash": "2c08343472791e6cf3c526fd10af405e6d64939fe0c46d5b9fe4fab44d007593",
  "private": false,
  "record": {
    "abstract": "This paper considers basic properties of super-operator norms induced by\nSchatten p-norms. Such super-operator norms arise in various contexts in the\nstudy of quantum information. It is proved that for completely positive\nsuper-operators, the value of any such norm is achieved by a positive\nsemidefinite input, answering a question recently posed by King and Ruskai.\nHowever, for any choice of p, there exists a super-operator that is the\ndifference of two completely positive, trace-preserving super-operators such\nthat the value of the super-operator norm is not even achieved on a Hermitian\ninput operator. Also considered are the properties of the above norms for\nsuper-operators tensored with the identity super-operator.",
    "arxiv_id": "quant-ph/0411077",
    "authors": [
      "John Watrous"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Notes on super-operator norms induced by Schatten norms",
    "url": "https://arxiv.org/abs/quant-ph/0411077"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cbdf29f5-1b7a-472e-8c62-1ec2a75c57d1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}