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    Weak mutually unbiased bases with applications to quantum cryptography and tomography. Weak mutually unbiased bases.

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    Publication date
    2013-12-05
    Author
    Shalaby, Mohamed Mahmoud Youssef
    Supervisor
    Vourdas, Apostolos
    Keyword
    Finite quantum systems
    Quantum tomography
    Quantum cryptography
    Weak mutually unbiased bases
    Hilbert spaces
    Rights
    Creative Commons License
    The University of Bradford theses are licenced under a Creative Commons Licence.
    Institution
    University of Bradford
    Department
    Department of Computing
    Awarded
    2012
    
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    Abstract
    Mutually unbiased bases is an important topic in the recent quantum system researches. Although there is much work in this area, many problems related to mutually unbiased bases are still open. For example, constructing a complete set of mutually unbiased bases in the Hilbert spaces with composite dimensions has not been achieved yet. This thesis defines a weaker concept than mutually unbiased bases in the Hilbert spaces with composite dimensions. We call this concept, weak mutually unbiased bases. There is a duality between such bases and the geometry of the phase space Zd × Zd, where d is the phase space dimension. To show this duality we study the properties of lines through the origin in Zd × Zd, then we explain the correspondence between the properties of these lines and the properties of the weak mutually unbiased bases. We give an explicit construction of a complete set of weak mutually unbiased bases in the Hilbert space Hd, where d is odd and d = p1p2; p1, p2 are prime numbers. We apply the concept of weak mutually unbiased bases in the context of quantum tomography and quantum cryptography.
    URI
    http://hdl.handle.net/10454/5754
    Type
    Thesis
    Qualification name
    PhD
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