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. / Egyptian government.
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/5754 |
| Date | January 2012 |
| Creators | Shalaby, Mohamed Mahmoud Youssef |
| Contributors | Vourdas, Apostolos |
| Publisher | University of Bradford, Department of Computing |
| Source Sets | Bradford Scholars |
| Language | English |
| Detected Language | English |
| Type | Thesis, doctoral, PhD |
| Rights | <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/"><img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png" /></a><br />The University of Bradford theses are licenced under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/">Creative Commons Licence</a>. |
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