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    An analytic representation of weak mutually unbiased bases

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    PhD Thesis (974.9Kb)
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    Publication date
    2016
    Author
    Olupitan, Tominiyi E.
    Supervisor
    Vourdas, Apostolos
    Ci, Lei
    Keyword
    Finite quantum systems
    Weak mutually unbiased bases
    Finite geometry
    Theta functions
    Rights
    Creative Commons License
    The University of Bradford theses are licenced under a Creative Commons Licence.
    Institution
    University of Bradford
    Department
    Faculty of Engineering and Informatics
    Awarded
    2016
    
    Metadata
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    Abstract
    Quantum systems in the d-dimensional Hilbert space are considered. The mutually unbiased bases is a deep problem in this area. The problem of finding all mutually unbiased bases for higher (non-prime) dimension is still open. We derive an alternate approach to mutually unbiased bases by studying a weaker concept which we call weak mutually unbiased bases. We then compare three rather different structures. The first is weak mutually unbiased bases, for which the absolute value of the overlap of any two vectors in two different bases is 1/√k (where k∣d) or 0. The second is maximal lines through the origin in the Z(d) × Z(d) phase space. The third is an analytic representation in the complex plane based on Theta functions, and their zeros. The analytic representation of the weak mutually unbiased bases is defined with the zeros examined. It is shown that there is a correspondence (triality) that links strongly these three apparently different structures. We give an explicit breakdown of this triality.
    URI
    http://hdl.handle.net/10454/15904
    Type
    Thesis
    Qualification name
    PhD
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