{
  "id": "1603.03896",
  "version": "v1",
  "published": "2016-03-12T11:50:06.000Z",
  "updated": "2016-03-12T11:50:06.000Z",
  "title": "Optimal non-invasive measurement of Full Counting Statistics by a single qubit",
  "authors": [
    "A. V. Lebedev",
    "G. B. Lesovik",
    "G. Blatter"
  ],
  "comment": "8 pages, 1 figure, Accepted for publication in PRB",
  "categories": [
    "cond-mat.mes-hall",
    "quant-ph"
  ],
  "abstract": "The complete characterisation of the charge transport in a mesoscopic device is provided by the Full Counting Statistics (FCS) $P_t(m)$, describing the amount of charge $Q = me$ transmitted during the time $t$. Although numerous systems have been theoretically characterized by their FCS, the experimental measurement of the distribution function $P_t(m)$ or its moments $\\langle Q^n \\rangle$ are rare and often plagued by strong back-action. Here, we present a strategy for the measurement of the FCS, more specifically its characteristic function $\\chi(\\lambda)$ and moments $\\langle Q^n \\rangle$, by a qubit with a set of different couplings $\\lambda_j$, $j = 1,\\dots,k,\\dots k+p$, $k = \\lceil n/2 \\rceil$, $p \\geq 0$, to the mesoscopic conductor. The scheme involves multiple readings of Ramsey sequences at the different coupling strengths $\\lambda_j$ and we find the optimal distribution for these couplings $\\lambda_j$ as well as the optimal distribution $N_j$ of $N = \\sum N_j$ measurements among the different couplings $\\lambda_j$. We determine the precision scaling for the moments $\\langle Q^n \\rangle$ with the number $N$ of invested resources and show that the standard quantum limit can be approached when many additional couplings $p\\gg 1$ are included in the measurement scheme.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-12T11:50:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "full counting statistics",
      "optimal non-invasive measurement",
      "single qubit",
      "optimal distribution",
      "standard quantum limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}