{
  "id": "quant-ph/0507045",
  "version": "v1",
  "published": "2005-07-05T16:09:14.000Z",
  "updated": "2005-07-05T16:09:14.000Z",
  "title": "On environment-assisted capacities of quantum channels",
  "authors": [
    "Andreas Winter"
  ],
  "comment": "9 pages revtex4, 1 stolen figure (eps)",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Following initial work by Gregoratti and Werner [J. Mod. Optics 50, 913-933, 2003 and quant-ph/0403092] and Hayden and King [quant-ph/0409026], we study the problem of the capacity of a quantum channel assisted by a \"friendly (channel) environment\" that can locally measure and communicate classical messages to the receiver. Previous work [quant-ph/0505038] has yielded a capacity formula for the quantum capacity under this kind of help from the environment. Here we study the problem of the environment-assisted classical capacity, which exhibits a somewhat richer structure (at least, it seems to be the harder problem). There are several, presumably inequivalent, models of the permitted local operations and classical communications between receiver and environment: one-way, arbitrary, separable and PPT POVMs. In all these models, the task of decoding a message amounts to discriminating a set of possibly entangled states between the two receivers, by a class of operations under some sort of locality constraint. After introducing the operational capacities outlined above, we show that a lower bound on the environment-assisted classical capacity is always half the logarithm of the input space dimension. Then we develop a few techniques to prove the existence of channels which meet this lower bound up to terms of much smaller order, even when PPT decoding measurements are allowed (assuming a certain superadditivity conjecture).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-05T16:09:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum channel",
      "environment-assisted capacities",
      "lower bound",
      "environment-assisted classical capacity",
      "input space dimension"
    ],
    "note": {
      "typesetting": "RevTeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005quant.ph..7045W"
    }
  }
}