Equiangular Lines and Antipodal Covers
| dc.comment.hidden | Hi Trevor, I made the changes that you noted, and submitted the new version of my thesis. Best wishes, Hamed | en |
| dc.contributor.author | Mirjalalieh Shirazi, Mirhamed | |
| dc.date.accessioned | 2010-09-22T14:02:27Z | |
| dc.date.available | 2010-09-22T14:02:27Z | |
| dc.date.issued | 2010-09-22T14:02:27Z | |
| dc.date.submitted | 2010 | |
| dc.description.abstract | It is not hard to see that the number of equiangular lines in a complex space of dimension $d$ is at most $d^{2}$. A set of $d^{2}$ equiangular lines in a $d$-dimensional complex space is of significant importance in Quantum Computing as it corresponds to a measurement for which its statistics determine completely the quantum state on which the measurement is carried out. The existence of $d^{2}$ equiangular lines in a $d$-dimensional complex space is only known for a few values of $d$, although physicists conjecture that they do exist for any value of $d$. The main results in this thesis are: \begin{enumerate} \item Abelian covers of complete graphs that have certain parameters can be used to construct sets of $d^2$ equiangular lines in $d$-dimen\-sion\-al space; \item we exhibit infinitely many parameter sets that satisfy all the known necessary conditions for the existence of such a cover; and \item we find the decompose of the space into irreducible modules over the Terwilliger algebra of covers of complete graphs. \end{enumerate} A few techniques are known for constructing covers of complete graphs, none of which can be used to construct covers that lead to sets of $d^{2}$ equiangular lines in $d$-dimensional complex spaces. The third main result is developed in the hope of assisting such construction. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/5493 | |
| dc.language.iso | en | en |
| dc.pending | false | en |
| dc.publisher | University of Waterloo | en |
| dc.subject | Algebraic Combinatorics | en |
| dc.subject | Quantum Computing | en |
| dc.subject | Graph Theory | en |
| dc.subject.program | Combinatorics and Optimization | en |
| dc.title | Equiangular Lines and Antipodal Covers | en |
| dc.type | Doctoral Thesis | en |
| uws-etd.degree | Doctor of Philosophy | en |
| uws-etd.degree.department | Combinatorics and Optimization | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |