{
  "id": "1110.5944",
  "version": "v2",
  "published": "2011-10-26T23:09:03.000Z",
  "updated": "2011-12-23T01:21:19.000Z",
  "title": "Communication cost of classically simulating a quantum channel with subsequent rank-1 projective measurement",
  "authors": [
    "Alberto Montina"
  ],
  "comment": "corrected some minor typos",
  "journal": "Phys. Rev. A 84, 060303(R) (2011)",
  "doi": "10.1103/PhysRevA.84.060303",
  "categories": [
    "quant-ph",
    "cs.IT",
    "math-ph",
    "math.IT",
    "math.MP"
  ],
  "abstract": "A process of preparation, transmission and subsequent projective measurement of a qubit can be simulated by a classical model with only two bits of communication and some amount of shared randomness. However no model for n qubits with a finite amount of classical communication is known at present. A lower bound for the communication cost can provide useful hints for a generalization. It is known for example that the amount of communication must be greater than c 2^n, where c~0.01. The proof uses a quite elaborate theorem of communication complexity. Using a mathematical conjecture known as the \"double cap conjecture\", we strengthen this result by presenting a geometrical and extremely simple derivation of the lower bound 2^n-1. Only rank-1 projective measurements are involved in the derivation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-23T01:21:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.67.Hk",
      "03.67.Lx"
    ],
    "keywords": [
      "communication cost",
      "quantum channel",
      "classically simulating",
      "lower bound",
      "quite elaborate theorem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review A",
      "year": 2011,
      "month": "Dec",
      "volume": 84,
      "number": 6,
      "pages": "060303"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhRvA..84f0303M"
    }
  }
}