{
  "annotation_id": "34e672b8-0a08-4528-820e-c4cdf38023c4",
  "date_created": "2026-03-02T18:02:33.715000Z",
  "date_modified": "2026-03-02T18:02:33.715000Z",
  "file_hash": "f1cc0dc183facddf3076f23fd93bdbc0cce201a604fafbafe9335d6448ca7e70",
  "private": false,
  "record": {
    "abstract": "How much unavoidable randomness is generated by a Positive Operator Valued\nMeasure (POVM)? We address this question using two complementary approaches.\nFirst we study the variance of a real variable associated to the POVM outcomes.\nIn this context we introduce an uncertainty operator which measures how much\nadditional noise is introduced by carrying out a POVM rather than a von Neumann\nmeasurement. We illustrate this first approach by studying the variances of\njoint estimates of \\sigma_x and \\sigma_z for spin 1/2 particles. We show that\nfor unbiased measurements the sum of these variances is lower bounded by 1. In\nour second approach we study the entropy of the POVM outcomes. In particular we\ntry to establish lower bounds on the entropy of the POVM outcomes. We\nillustrate this second approach by examples.",
    "arxiv_id": "quant-ph/0703036",
    "authors": [
      "Serge Massar"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.76.042114",
    "journal_ref": "Phys. Rev. A 76, 042114 (2007)",
    "title": "Uncertainty Relations for Positive Operator Valued Measures",
    "url": "https://arxiv.org/abs/quant-ph/0703036"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2f74695d-090d-481d-8125-6cf714955cb2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}