{
  "id": "2407.14577",
  "version": "v1",
  "published": "2024-07-19T17:43:27.000Z",
  "updated": "2024-07-19T17:43:27.000Z",
  "title": "Quantum state tomography on closed timelike curves using weak measurements",
  "authors": [
    "Lachlan G. Bishop",
    "Fabio Costa",
    "Timothy C. Ralph"
  ],
  "comment": "17 pages, 9 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Any given prescription of quantum time travel necessarily endows a Hilbert space to the chronology-violating (CV) system on the closed timelike curve (CTC). However, under the two foremost models, Deutsch's prescription (D-CTCs) and postselected teleportation (P-CTCs), the CV system is treated very differently: D-CTCs assign a definite form to the state on this system, while P-CTCs do not. To further explore this distinction, we present a methodology by which an operational notion of state may be assigned to their respective CV systems. This is accomplished via a conjunction of state tomography and weak measurements, with the latter being essential in leaving any notions of self-consistency intact. With this technique, we are able to verify the predictions of D-CTCs and, perhaps more significantly, operationally assign a state to the system on the P-CTC. We show that, for any given combination of chronology-respecting input and unitary interaction, it is always possible to recover the unique state on the P-CTC, and we provide a few specific examples in the context of select archetypal temporal paradoxes. We also demonstrate how this state may be derived from analysis of the P-CTC prescription itself, and we explore how it compares to its counterpart in the CV state predicted by D-CTCs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-19T17:43:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "closed timelike curve",
      "quantum state tomography",
      "weak measurements",
      "quantum time travel necessarily endows",
      "cv system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}