Two orthonormal bases in the complex space of dimension d, are said to be mutually unbiased if the square of the magnitude of the inner product of any vector from one basis with any vector in other basis is equal to the reciprocal of the dimension
d. Mutually unbiased bases are used for optimal state determination of mixed quantum states.
It is known that in any dimension d, the number of mutually unbiased bases is at most d+1. Ivanovic found a complete set of mutually unbiased bases for prime dimensions. His construction was generalized by
Wootters and Fields for prime power dimensions. There is a strong connection between maximally commuting bases of orthogonal unitary
matrices and mutually unbiased bases. Based on this connection, there exits a constructive proof of the existence of a complete set of mutually unbiased bases for prime power dimensions. This thesis is an exploration on construction of mutually unbiased bases.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:MWU.1993/22109 |
| Date | 26 August 2013 |
| Creators | Taghikhani, Rahim |
| Contributors | Craigen, Robert (Mathematics), Chipalkatti, Jaydeep (Mathematics) Li, Ben Pak Ching (Computer Science) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Detected Language | English |
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