{
  "annotation_id": "4ca93b18-845a-41fb-8e53-fb38c77bc060",
  "date_created": "2026-03-02T18:01:56.125000Z",
  "date_modified": "2026-03-02T18:01:56.125000Z",
  "file_hash": "fd6034654601231d2cd373ac9333006883c5208154abe3b3371aa4d31b982b14",
  "private": false,
  "record": {
    "abstract": "We develop a sufficient condition for the least-squares measurement (LSM), or\nthe square-root measurement, to minimize the probability of a detection error\nwhen distinguishing between a collection of mixed quantum states. Using this\ncondition we derive the optimal measurement for state sets with a broad class\nof symmetries.\n  We first consider geometrically uniform (GU) state sets with a possibly\nnonabelian generating group, and show that if the generator satisfies a certain\nconstraint, then the LSM is optimal. In particular, for pure-state GU ensembles\nthe LSM is shown to be optimal. For arbitrary GU state sets we show that the\noptimal measurement operators are GU with generator that can be computed very\nefficiently in polynomial time, within any desired accuracy.\n  We then consider compound GU (CGU) state sets which consist of subsets that\nare GU. When the generators satisfy a certain constraint, the LSM is again\noptimal. For arbitrary CGU state sets the optimal measurement operators are\nshown to be CGU with generators that can be computed efficiently in polynomial\ntime.",
    "arxiv_id": "quant-ph/0211111",
    "authors": [
      "Yonina C. Eldar",
      "Alexandre Megretski",
      "George C. Verghese"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Optimal Detection of Symmetric Mixed Quantum States",
    "url": "https://arxiv.org/abs/quant-ph/0211111"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1113f62c-f10e-4888-8bf7-7e8e4f161588",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}