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  • About SIC POVMs and discrete Wigner distributions

    Author(s)
    Colin, Samuel
    Corbett, John
    Durt, Thomas
    Gross, David
    Griffith University Author(s)
    Colin, Samuel
    Year published
    2005
    Metadata
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    Abstract
    A set of d2 vectors in a Hilbert space of dimension d is called equiangular if each pair of vectors encloses the same angle. The projection operators onto these vectors define a POVM which is distinguished by its high degree of symmetry. Measures of this kind are called symmetric informationally complete, or SIC POVMs for short, and could be applied for quantum state tomography. Despite its simple geometrical description, the problem of constructing SIC POVMs or even proving their existence seems to be very hard. It is our purpose to introduce two applications of discrete Wigner functions to the analysis of the problem ...
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    A set of d2 vectors in a Hilbert space of dimension d is called equiangular if each pair of vectors encloses the same angle. The projection operators onto these vectors define a POVM which is distinguished by its high degree of symmetry. Measures of this kind are called symmetric informationally complete, or SIC POVMs for short, and could be applied for quantum state tomography. Despite its simple geometrical description, the problem of constructing SIC POVMs or even proving their existence seems to be very hard. It is our purpose to introduce two applications of discrete Wigner functions to the analysis of the problem at hand. First, we will present a method for identifying symmetries of SIC POVMs under Clifford operations. This constitutes an alternative approach to a structure describedbefore by Zauner and Appleby. Further, a simple and geometrically motivated construction for an SIC POVM in dimensions two and three is given (which, unfortunately, allows no generalization). Even though no new structures are found, we hope that the re-formulation of the problem may prove useful for future inquiries.
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    Journal Title
    Journal of Optics B: Quantum and semiclassical optics
    Volume
    7
    DOI
    https://doi.org/10.1088/1464-4266/7/12/051
    Subject
    Quantum Information, Computation and Communication
    Publication URI
    http://hdl.handle.net/10072/32522
    Collection
    • Journal articles

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