{
  "annotation_id": "af8738d0-9e00-484e-b8d3-2df0e9228cd2",
  "date_created": "2026-03-02T18:01:39.267000Z",
  "date_modified": "2026-03-02T18:01:39.267000Z",
  "file_hash": "54fdd7d0284487edec39d04f2b33b6d6a6cb8e8eaf8c030c89c38a9d3b3c6187",
  "private": false,
  "record": {
    "abstract": "Topological and geometrical properties of the set of mixed quantum states in\nthe N-dimensional Hilbert space are analysed. Assuming that the corresponding\nclassical dynamics takes place on the sphere we use the vector SU(2) coherent\nstates and the generalised Husimi distributions to define the Monge distance\nbetween arbitrary two density matrices. The Monge metric has a simple\nsemiclassical interpretation and induces a non-trivial geometry. Among all pure\nstates the distance from the maximally mixed state \\rho_*, proportional to the\nidentity matrix, admits the largest value for the coherent states, while the\ndelocalized \u0027chaotic\u0027 states are close to \\rho_*. This contrasts the geometries\ninduced by the standard (trace, Hilbert-Schmidt or Bures) metrics, where the\ndistance from \\rho_* is the same for all pure states. We discuss possible\nphysical consequences including unitary time evolution and the process of\ndecoherence. We introduce also a simplified Monge metric, defined in the space\nof pure quantum states, and more suitable for numerical computation.",
    "arxiv_id": "quant-ph/0008016",
    "authors": [
      "Karol Zyczkowski",
      "Wojciech Slomczynski"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/34/34/311",
    "journal_ref": "J. Phys. A34, 6689-6722 (2001)",
    "title": "Monge Metric on the Sphere and Geometry of Quantum States",
    "url": "https://arxiv.org/abs/quant-ph/0008016"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a99b5e13-b14a-4af9-885e-6b9352f49652",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}