{
  "id": "0710.0285",
  "version": "v2",
  "published": "2007-10-01T18:59:42.000Z",
  "updated": "2007-10-20T22:47:46.000Z",
  "title": "Quantum-limited metrology with product states",
  "authors": [
    "Sergio Boixo",
    "Animesh Datta",
    "Steven T. Flammia",
    "Anil Shaji",
    "Emilio Bagan",
    "Carlton M. Caves"
  ],
  "comment": "15 pages, 6 figures",
  "journal": "Phys. Rev. A 77, 012317 (2007)",
  "doi": "10.1103/PhysRevA.77.012317",
  "categories": [
    "quant-ph",
    "cond-mat.other"
  ],
  "abstract": "We study the performance of initial product states of n-body systems in generalized quantum metrology protocols that involve estimating an unknown coupling constant in a nonlinear k-body (k << n) Hamiltonian. We obtain the theoretical lower bound on the uncertainty in the estimate of the parameter. For arbitrary initial states, the lower bound scales as 1/n^k, and for initial product states, it scales as 1/n^(k-1/2). We show that the latter scaling can be achieved using simple, separable measurements. We analyze in detail the case of a quadratic Hamiltonian (k = 2), implementable with Bose-Einstein condensates. We formulate a simple model, based on the evolution of angular-momentum coherent states, which explains the O(n^(-3/2)) scaling for k = 2; the model shows that the entanglement generated by the quadratic Hamiltonian does not play a role in the enhanced sensitivity scaling. We show that phase decoherence does not affect the O(n^(-3/2)) sensitivity scaling for initial product states.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-10-20T22:47:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.67.Lx",
      "03.65.Ta",
      "06.20.Dk"
    ],
    "keywords": [
      "initial product states",
      "quantum-limited metrology",
      "quadratic hamiltonian",
      "angular-momentum coherent states",
      "arbitrary initial states"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review A",
      "year": 2008,
      "month": "Jan",
      "volume": 77,
      "number": 1,
      "pages": "012317"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhRvA..77a2317B"
    }
  }
}