Permutationally invariant state reconstruction

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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  • Author: Moroder, Tobias

    Universität Siegen, Naturwissenschaftlich-Technische Fakultät, Germany

  • Author: Hyllus, Philipp

    University of the Basque Country, Spain

  • Author: Tóth, Géza

    University of the Basque Country, Spain

  • Author: Schwemmer, Christian

    Max Planck Institute, Germany

  • Author: Niggebaum, Alexander

    Max Planck Institute, Germany

  • Author: Gaile, Stefanie

    Department of Mathematics, Technical University of Denmark

  • Author: Gühne, Otfried

    Universität Siegen, Naturwissenschaftlich-Technische Fakultät, Germany

  • Author: Weinfurter, Harald

    Max Planck Institute, Germany

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Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations easily allow reconstruction of a state of 20 qubits in a few minutes on a standard computer.
Original languageEnglish
JournalNew Journal of Physics
Volume14
Issue number10
Pages (from-to)105001
Number of pages26
ISSN1367-2630
DOIs
StatePublished - 2012
Peer-reviewedYes
CitationsWeb of Science® Times Cited: 16

Keywords

  • State reconstruction, quantum tomography , General statistical methods , Operator theory , Numerical optimization
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