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    Partial ordering of weak mutually unbiased bases in finite quantum systems

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    PhD Thesis (654.9Kb)
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    Publication date
    2015
    Author
    Oladejo, Semiu Oladipupo
    Supervisor
    Vourdas, Apostolos
    Lei, Ci
    Keyword
    Finite quantum systems; Weak mutually unbiased bases; Finite geometry
    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 School of Electrical Engineering and Computer Science
    Awarded
    2015
    
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    Abstract
    There has being an enormous work on finite quantum systems with variables in Zd, especially on mutually unbiased bases. The reason for this is due to its wide areas of application. We focus on partial ordering of weak mutually un-biased bases. In it, we studied a partial ordered relation which exists between a subsystem ^(q) and a larger system ^(d) and also, between a subgeometry Gq and larger geometry Gd. Furthermore, we show an isomorphism between: (i) the set {Gd} of subgeometries of a finite geometry Gd and subsets of the set {D(d)} of divisors of d. (ii) the set {hd} of subspaces of a finite Hilbert space Hd and subsets of the set {D(d)} of divisors of d. (iii) the set {Y(d)} of subsystems of a finite quantum system ^(d) and subsets of the set {D(d)} of divisors of d. We conclude this work by showing a duality between lines in finite geometry Gd and weak mutually unbiased bases in finite dimensional Hilbert space Hd.
    URI
    http://hdl.handle.net/10454/14641
    Type
    Thesis
    Qualification name
    PhD
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