MSc Math Defence: Operator Theory and Quantum Local Operations and Classical Communication Conditions

Comfort Mintah, M.Sc. thesis defence

This thesis begins by discussing the finite dimensional C*-algebras and their representation theory. We describe local operations and classical communication (LOCC ) in quantum information theory. We begin with the physical description of LOCC and its schematics, and then give the description. We restrict ourselves to one-way LOCC and discuss detailed analysis in quantum information of recently derived operator relations. We indicate how operator structures such as operator systems, operator algebras, and Hilbert C*-modules all naturally arise in this setting, and we make use of these structures to derive new results and derivation in the study of one-way LOCC. We establish results comparing perfect distinguishability of one-way LOCC verses arbitrary quantum operations, and show they are equivalent for several families of operators that appear jointly in matrix and operator theory and quantum information theory.