{
  "id": "1802.07744",
  "version": "v1",
  "published": "2018-02-21T19:00:17.000Z",
  "updated": "2018-02-21T19:00:17.000Z",
  "title": "Contextuality bounds the efficiency of classical simulation of quantum processes",
  "authors": [
    "Angela Karanjai",
    "Joel J. Wallman",
    "Stephen D. Bartlett"
  ],
  "comment": "6 pages, comments welcome",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Contextuality has been conjectured to be a super-classical resource for quantum computation, analogous to the role of non-locality as a super-classical resource for communication. We show that the presence of contextuality places a lower bound on the amount of classical memory required to simulate any quantum sub-theory, thereby establishing a quantitative connection between contextuality and classical simulability. We apply our result to the qubit stabilizer sub-theory, where the presence of state-independent contextuality has been an obstacle in establishing contextuality as a quantum computational resource. We find that the presence of contextuality in this sub-theory demands that the minimum number of classical bits of memory required to simulate a multi-qubit system must scale quadratically in the number of qubits; notably, this is the same scaling as the Gottesman-Knill algorithm. We contrast this result with the (non-contextual) qudit case, where linear scaling is possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-21T19:00:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum processes",
      "contextuality bounds",
      "classical simulation",
      "efficiency",
      "qubit stabilizer sub-theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}