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Title: Weak mutually unbiased bases with applications to quantum cryptography and tomography
Author: Shalaby, Mohamed Mahmoud Youssef
ISNI:       0000 0004 2747 9349
Awarding Body: University of Bradford
Current Institution: University of Bradford
Date of Award: 2012
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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.
Supervisor: Vourdas, Apostolos Sponsor: Egyptian Government
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Finite quantum systems ; Quantum tomography ; Quantum cryptography ; Weak mutually unbiased bases ; Hilbert spaces