# Operator Theory and Conditions for Quantum Local Operations and Classical Communication

 Title: Operator Theory and Conditions for Quantum Local Operations and Classical Communication Mintah, Comfort Department of Mathematics and Statistics Mathematics and Statistics Kribs, David 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}. http://hdl.handle.net/10214/10213 2016-12 Attribution-NonCommercial-ShareAlike 2.5 Canada All items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated.
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