Permutationally invariant state reconstruction

Tobias Moroder, Philipp Hyllus, Géza Tóth, Christian Schwemmer, Alexander Niggebaum, Stefanie Gaile, Otfried Gühne, Harald Weinfurter

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    Abstract

    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
    Publication statusPublished - 2012

    Keywords

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

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