Essec\Faculty\Model\Contribution {#2233
  #_index: "academ_contributions"
  #_id: "13895"
  #_source: array:26 [
    "id" => "13895"
    "slug" => "pseudo-bayesian-quantum-tomography-with-rank-adaptation"
    "yearMonth" => "2017-05"
    "year" => "2017"
    "title" => "Pseudo-Bayesian quantum tomography with rank-adaptation"
    "description" => "MAI, T.T. et ALQUIER, P. (2017). Pseudo-Bayesian quantum tomography with rank-adaptation. <i>Journal of Statistical Planning and Inference</i>, 184, pp. 62-76."
    "authors" => array:2 [
      0 => array:3 [
        "name" => "ALQUIER Pierre"
        "bid" => "B00809923"
        "slug" => "alquier-pierre"
      ]
      1 => array:1 [
        "name" => "MAI The Tien"
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:5 [
      0 => "Quantum statistics"
      1 => "Bayesian statistics"
      2 => "PAC-Bayesian bounds"
      3 => "Oracle inequalities"
      4 => "MCMC"
    ]
    "updatedAt" => "2023-03-22 09:51:22"
    "publicationUrl" => "https://doi.org/10.1016/j.jspi.2016.11.003"
    "publicationInfo" => array:3 [
      "pages" => "62-76"
      "volume" => "184"
      "number" => ""
    ]
    "type" => array:2 [
      "fr" => "Articles"
      "en" => "Journal articles"
    ]
    "support_type" => array:2 [
      "fr" => "Revue scientifique"
      "en" => "Scientific journal"
    ]
    "countries" => array:2 [
      "fr" => null
      "en" => null
    ]
    "abstract" => array:2 [
      "fr" => "Quantum state tomography, an important task in quantum information processing, aims at reconstructing a state from prepared measurement data. Bayesian methods are recognized to be one of the good and reliable choices in estimating quantum states (Blume-Kohout, 2010). Several numerical works showed that Bayesian estimations are comparable to, and even better than other methods in the problem of 1-qubit state recovery. However, the problem of choosing prior distribution in the general case of n qubits is not straightforward. More importantly, the statistical performance of Bayesian type estimators has not been studied from a theoretical perspective yet. In this paper, we propose a novel prior for quantum states (density matrices), and we define pseudo-Bayesian estimators of the density matrix. Then, using PAC-Bayesian theorems (Catoni, 2007), we derive rates of convergence for the posterior mean. The numerical performance of these estimators is tested on simulated and real datasets."
      "en" => "Quantum state tomography, an important task in quantum information processing, aims at reconstructing a state from prepared measurement data. Bayesian methods are recognized to be one of the good and reliable choices in estimating quantum states (Blume-Kohout, 2010). Several numerical works showed that Bayesian estimations are comparable to, and even better than other methods in the problem of 1-qubit state recovery. However, the problem of choosing prior distribution in the general case of n qubits is not straightforward. More importantly, the statistical performance of Bayesian type estimators has not been studied from a theoretical perspective yet. In this paper, we propose a novel prior for quantum states (density matrices), and we define pseudo-Bayesian estimators of the density matrix. Then, using PAC-Bayesian theorems (Catoni, 2007), we derive rates of convergence for the posterior mean. The numerical performance of these estimators is tested on simulated and real datasets."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2024-12-21T16:21:43.000Z"
    "docTitle" => "Pseudo-Bayesian quantum tomography with rank-adaptation"
    "docSurtitle" => "Articles"
    "authorNames" => "<a href="/cv/alquier-pierre">ALQUIER Pierre</a>, MAI The Tien"
    "docDescription" => "<span class="document-property-authors">ALQUIER Pierre, MAI The Tien</span><br><span class="document-property-authors_fields">Systèmes d'Information, Data Analytics et Opérations</span> | <span class="document-property-year">2017</span>"
    "keywordList" => "<a href="#">Quantum statistics</a>, <a href="#">Bayesian statistics</a>, <a href="#">PAC-Bayesian bounds</a>, <a href="#">Oracle inequalities</a>, <a href="#">MCMC</a>"
    "docPreview" => "<b>Pseudo-Bayesian quantum tomography with rank-adaptation</b><br><span>2017-05 | Articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://doi.org/10.1016/j.jspi.2016.11.003" target="_blank">Pseudo-Bayesian quantum tomography with rank-adaptation</a>"
  ]
  +lang: "fr"
  +"_type": "_doc"
  +"_score": 8.755391
  +"parent": null
}