{
  "id": "2312.17744",
  "version": "v2",
  "published": "2023-12-29T18:57:32.000Z",
  "updated": "2024-06-18T18:03:50.000Z",
  "title": "Universality classes for purification in nonunitary quantum processes",
  "authors": [
    "Andrea De Luca",
    "Chunxiao Liu",
    "Adam Nahum",
    "Tianci Zhou"
  ],
  "comment": "22 pages, 13 figures, many improvements for clarity in v2, inc extended introductory text, new figures and one more technical appendix",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "cond-mat.str-el"
  ],
  "abstract": "We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\\ldots m_1}$ of many large random matrices. Each kind of process is associated with the decay of natural measures of entropy as a function of time or of the number of matrices in the product. We argue that, for a broad class of models, each process is described by universal scaling forms for purification, and that (i) and (ii) represent distinct ``universality classes'' with distinct scaling functions. Using the replica trick, these universality classes correspond to one-dimensional effective statistical mechanics models for a gas of ``kinks'', representing domain walls between elements of the permutation group. (This is an instructive low-dimensional limit of the effective statistical mechanics models for random circuits and tensor networks.) These results apply to long-time purification in spatially local monitored circuit models on the entangled side of the measurement phase transition.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-06-18T18:03:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "universality classes",
      "nonunitary quantum processes",
      "effective statistical mechanics models",
      "purification",
      "large random matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}