{
  "id": "1808.08639",
  "version": "v1",
  "published": "2018-08-26T23:01:38.000Z",
  "updated": "2018-08-26T23:01:38.000Z",
  "title": "Strong and Weak Optimizations in Classical and Quantum Models of Stochastic Processes",
  "authors": [
    "Samuel Loomis",
    "James P. Crutchfield"
  ],
  "comment": "14 pages, 14 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/uemum.htm",
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "Among the predictive hidden Markov models that describe a given stochastic process, the {\\epsilon}-machine is strongly minimal in that it minimizes every R\\'enyi-based memory measure. Quantum models can be smaller still. In contrast with the {\\epsilon}-machine's unique role in the classical setting, however, among the class of processes described by pure-state hidden quantum Markov models, there are those for which there does not exist any strongly minimal model. Quantum memory optimization then depends on which memory measure best matches a given problem circumstance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-26T23:01:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum models",
      "stochastic process",
      "weak optimizations",
      "pure-state hidden quantum markov models",
      "memory measure best matches"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}