{
  "id": "quant-ph/0108076",
  "version": "v2",
  "published": "2001-08-16T16:52:34.000Z",
  "updated": "2002-05-20T16:51:33.000Z",
  "title": "Optimal simulation of nonlocal Hamiltonians using local operations and classical communication",
  "authors": [
    "G. Vidal",
    "J. I. Cirac"
  ],
  "comment": "10 pages, 1 figure, revtex, major changes in presentation, results unchanged",
  "journal": "Phys. Rev. A 66, 022315 (2002)",
  "doi": "10.1103/PhysRevA.66.022315",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Consider a set of $N$ systems and an arbitrary interaction Hamiltonian $H$ that couples them. We investigate the use of local operations and classical communication (LOCC), together with the Hamiltonian $H$, to simulate a unitary evolution of the $N$ systems according to some other Hamiltonian $H'$. First, we show that the most general simulation using $H$ and LOCC can be also achieved, with the same time efficiency, by just interspersing the evolution of $H$ with local unitary manipulations of each system and a corresponding local ancilla (in a so-called LU+anc protocol). Thus, the ability to make local measurements and to communicate classical information does not help in non--local Hamiltonian simulation. Second, we show that both for the case of two $d$-level systems ($d>2$), or for that of a setting with more than two systems ($N>2$), LU+anc protocols are more powerful than LU protocols. Therefore local ancillas are a useful resource for non--local Hamiltonian simulation. Third, we use results of majorization theory to explicitly solve the problem of optimal simulation of two-qubit Hamiltonians using LU (equivalently, LU+anc, LO or LOCC).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-05-20T16:51:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local operations",
      "optimal simulation",
      "classical communication",
      "nonlocal hamiltonians",
      "non-local hamiltonian simulation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. A"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}