An invitation to quantum tomography

L.M. Artiles, R.D. Gill, M.I. Guta

    Research output: Contribution to journalArticleAcademicpeer-review

    55 Citations (Scopus)

    Abstract

    We describe quantum tomography as an inverse statistical problem in which the quantum state of a light beam is the unknown parameter and the data are given by results of measurements performed on identical quantum systems. The state can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We present consistency results for pattern function projection estimators and for sieve maximum likelihood estimators for both the density matrix of the quantum state and its Wigner function. We illustrate the performance of the estimators on simulated data. An EM algorithm is proposed for practical implementation. There remain many open problems, e.g. rates of convergence, adaptation and studying other estimators; a main purpose of the paper is to bring these to the attention of the statistical community.
    Original languageEnglish
    Pages (from-to)109-134
    JournalJournal of the Royal Statistical Society. Series B : Statistical Methodology
    Volume67
    Issue number1
    DOIs
    Publication statusPublished - 2005

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