Choice of measurement sets in qubit tomography

Mark D. De Burgh, Nathan K. Langford, Andrew C. Doherty, Alexei Gilchrist

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    Abstract

    Optimal generalized measurements for state estimation are well understood. However, practical quantum state tomography is typically performed using a fixed set of projective measurements, and the question of how to choose these measurements has been largely unexplored in the literature. In this work, we develop theoretical asymptotic bounds for the average fidelity of pure qubit tomography using measurement sets whose axes correspond to faces of Platonic solids. We also present comprehensive simulations of maximum likelihood tomography for mixed qubit states using the Platonic solid measurements. We show that overcomplete measurement sets can be used to improve the accuracy of tomographic reconstructions.

    Original languageEnglish
    Article number052122
    Pages (from-to)1-15
    Number of pages15
    JournalPhysical Review A - Atomic, Molecular, and Optical Physics
    Volume78
    Issue number5
    DOIs
    Publication statusPublished - 26 Nov 2008

    Bibliographical note

    Mark D. de Burgh, Nathan K. Langford, Andrew C. Doherty, and Alexei Gilchrist, Physical review A, Vol. 78, Article 052122, 2008. Copyright 2008 by the American Physical Society. The original article can be found at http://link.aps.org/doi/10.1103/PhysRevA.78.052122

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