Cleve, Richard E.de Beaudrap, Jonathan Robert Niel2005-08-192005-08-192004de Beaudrap, J. R. (2004). Applying quantum information to fingerprinting schemes and algebraic structures (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/187040612933652http://hdl.handle.net/1880/42311Bibliography: p. 280-283This research consists of three topics in quantum information science. First is an examination of the advantages that quantum information gives over classical information in very small instances of the fingerprinting problem. The second topic presents the properties of quantum Fourier transforms (QFTs) with respect to finite abelian groups, extends these ideas to finite unitary rings, and demonstrates how these properties characterize QFTs. The final topic applies some of the properties of the QFT to solve an oracle problem defined in terms of scrambled or "hidden" polynomial functions. Understanding quantum information often requires a major change in perspective, and thus has a reputation of being very difficult. Muddled and vague "popular presentations" contribute to the problem. In reaction to these issues, an introduction is presented here which relies on mathematics and supplementary commentary to present the ideas of quantum information, suitable for any reader with basic knowledge of linear algebra.xxiv, 312 leaves : ill. ; 30 cm.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.master thesis10.11575/PRISM/18704AC1 .T484 2004 D43