{
  "annotation_id": "92df5b58-7b1a-4258-8b77-2fc5e31214c6",
  "date_created": "2026-03-02T18:02:10.329000Z",
  "date_modified": "2026-03-02T18:02:10.329000Z",
  "file_hash": "525c2c9348bcab78913aa3be52641b05ba2aae87998b9971a78ff086078a13f0",
  "private": false,
  "record": {
    "abstract": "The scheme for construction of distances, presented in the previous paper\nquant-ph/0005087, v.1 (Ref. 1) is amended. The formulation of Proposition 1 of\nRef. 1 does not ensure the triangle inequality, therefore some of the\nfunctionals D(a,b) in Ref. 1 are in fact quasi-distances. In this note we\nformulate sufficient conditions for a functional D(a,b) of the (squared) form\nD(a,b)^2 = f(a)^2 + f(b)^2 - 2f(a)f(b)g(a,b) to be a distance and provide some\nexamples of such distances. A one parameter generalization of a bounded\ndistance of the (squared) form D(a,b)^2 = D_0^2 (1 - g(a,b)), which includes\nthe known Bures-Uhlmann and Hilbert-Schmidt distances between quantum states,\nis established.",
    "arxiv_id": "quant-ph/0410045",
    "authors": [
      "D. A. Trifonov"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "On the \u0027Polarized distances between quantum states and observables\u0027",
    "url": "https://arxiv.org/abs/quant-ph/0410045"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2df3bb45-f092-4357-9252-2c3ee2f08b9f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}