{
  "id": "quant-ph/0404145",
  "version": "v1",
  "published": "2004-04-26T14:25:47.000Z",
  "updated": "2004-04-26T14:25:47.000Z",
  "title": "Knowledge excess duality and violation of Bell inequalities",
  "authors": [
    "R. Filip",
    "M. Gavenda"
  ],
  "comment": "5 pages and 1 figure",
  "categories": [
    "quant-ph"
  ],
  "abstract": "A constraint on two complementary knowledge excesses by maximal violation of Bell inequalities for a single copy of any mixed state of two qubits $S,M$ is analyzed. The complementary knowledge excesses ${\\bf \\Delta K}(\\Pi_{M}\\to \\Pi_{S})$ and ${\\bf \\Delta K}(\\Pi'_{M}\\to \\Pi'_{S})$ quantify an enhancement of ability to predict results of the complementary projective measurements $\\Pi_{S},\\Pi'_{S}$ on the qubit $S$ from the projective measurements $\\Pi_{M},\\Pi'_{M}$ performed on the qubit $M$. For any state $\\rho_{SM}$ and for arbitrary $\\Pi_{S},\\Pi'_{S}$ and $\\Pi_{M},\\Pi'_{M}$, the knowledge excesses satisfy the following inequality ${\\bf \\Delta K}^{2}(\\Pi_{M}\\to \\Pi_{S})+{\\bf \\Delta K}^{2} (\\Pi'_{M}\\to \\Pi'_{S})\\leq (B_{max}/2)^2$, where $B_{max}$ is maximum of violation of Bell inequalities under single-copy local operations (local filtering and unitary transformations). Particularly, for the Bell-diagonal states only an appropriate choice of the measurements $\\Pi_{S},\\Pi'_{S}$ and $\\Pi_{M},\\Pi'_{M}$ are sufficient to saturate the inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-26T14:25:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inequality",
      "bell inequalities",
      "knowledge excess duality",
      "complementary knowledge excesses",
      "single-copy local operations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004quant.ph..4145F"
    }
  }
}