Operator Theory and Conditions for Quantum Local Operations and Classical Communication

 dc.contributor.advisor Kribs, David dc.contributor.author Mintah, Comfort dc.date.accessioned 2017-01-16T19:57:15Z dc.date.available 2017-01-16T19:57:15Z dc.date.copyright 2016-12 dc.date.created 2016-12-20 dc.date.issued 2017-01-16 dc.identifier.uri http://hdl.handle.net/10214/10213 dc.description.abstract We study the finite dimensional $C^{*}$-algebras and their representation theory. The physical description of quantum local operations and classical communication (LOCC) and its schematics are presented. Focusing on the mathematical description of one-way LOCC, we give detailed analysis of recently derived operator relations in quantum information theory. We also show how functional analytic tools such as operatorx systems, operator algebras, and Hilbert $C^{*}$-modules all naturally emerge in this setting. We make use of these structures to derive some key results in one-way LOCC. Perfect distinguishability of one-way LOCC versus arbitrary quantum operations is analyzed. It turns out that they are equivalent for several families of operators that appear jointly in matrix and operator theory and quantum information theory. The main results of this work are contained in the paper \citep{comfort}. en_US dc.description.sponsorship AIMS-Next Einstein and University of Guelph en_US dc.language.iso en en_US dc.rights Attribution-NonCommercial-ShareAlike 2.5 Canada * dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/2.5/ca/ * dc.subject Operator Theory en_US dc.subject LOCC condition en_US dc.title Operator Theory and Conditions for Quantum Local Operations and Classical Communication en_US dc.type Thesis en_US dc.degree.programme Mathematics and Statistics en_US dc.degree.name Master of Science en_US dc.degree.department Department of Mathematics and Statistics en_US dc.rights.license All items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated.
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