{
  "annotation_id": "66bfe574-cb6f-4d12-9da2-17262af47c96",
  "date_created": "2026-03-02T18:02:20.542000Z",
  "date_modified": "2026-03-02T18:02:20.542000Z",
  "file_hash": "409fac7a323a4cae8dc38bdccccdd38ac587b405ecd52473d4b98c3833a8c987",
  "private": false,
  "record": {
    "abstract": "A system of diagrams is introduced that allows the representation of various\nelements of a quantum circuit, including measurements, in a form which makes no\nreference to time (hence ``atemporal\u0027\u0027). It can be used to relate quantum\ndynamical properties to those of entangled states (map-state duality), and\nsuggests useful analogies, such as the inverse of an entangled ket. Diagrams\nclarify the role of channel kets, transition operators, dynamical operators\n(matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite)\noperators are represented by diagrams with a symmetry that aids in\nunderstanding their connection with completely positive maps. The diagrams are\nused to analyze standard teleportation and dense coding, and for a careful\nstudy of unambiguous (conclusive) teleportation. A simple diagrammatic argument\nshows that a Kraus rank of 3 is impossible for a one-qubit channel modeled\nusing a one-qubit environment in a mixed state.",
    "arxiv_id": "quant-ph/0507215",
    "authors": [
      "Robert B. Griffiths",
      "Shengjun Wu",
      "Li Yu",
      "Scott M. Cohen"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.73.052309",
    "journal_ref": "Physical Review A 73, 052309 (2006)",
    "title": "Atemporal diagrams for quantum circuits",
    "url": "https://arxiv.org/abs/quant-ph/0507215"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4de197ba-beb2-483c-95fe-3352bdccb3fb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}