{
  "annotation_id": "0b642882-44ee-4974-ba02-1d4240f7629b",
  "date_created": "2026-03-02T18:01:38.356000Z",
  "date_modified": "2026-03-02T18:01:38.356000Z",
  "file_hash": "3b24ff29f0752b339d602bf6ca8b12d5f043f9dac9e940871c29cf18ecef1804",
  "private": false,
  "record": {
    "abstract": "We discuss complementarity and uncertainty in a gedanken Which-Way\n(Welcher-Weg) experiment in a Mach-Zehnder interferometer. Although a\nWelcher-Weg measurement can be performed with only a negligible amount of\nmomentum change in the detector itself, the change in the interference pattern\nmust correspond to a change in the momentum distribution of the particle.\nEntanglement between the Mach-Zehnder interferometer and the Welcher-Weg\nmeasurement introduces orthogonality that disables the interference of the\nparticle, but simultaneously, it also generates a momentum transfer between the\nparticle and other parts of the whole entangled system (including macroscopic\nparts). This analysis can be related to the Delayed Choice interpretation. We\nshow where the momentum change takes place and we conclude that entanglement is\nthe key to understand how complementarity (i.e. Which Way versus interference)\nand the position-momentum uncertainty relation are interwoven.",
    "arxiv_id": "quant-ph/0008096",
    "authors": [
      "D. Ludwin",
      "Y. Ben-Aryeh",
      "A. Mann"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum Optical Discussion of Uncertainty and Complementarity in a   Mach-Zehnder Interferometer",
    "url": "https://arxiv.org/abs/quant-ph/0008096"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6497bf51-d075-45f5-bef1-68c92c3c6675",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}