Special classes of completely positive linear maps

dc.contributor.advisorPereira, Rajesh
dc.contributor.authorO'Meara, Corey Patrick
dc.date.accessioned2020-12-04T16:03:14Z
dc.date.available2020-12-04T16:03:14Z
dc.date.copyright2010
dc.degree.departmentDepartment of Mathematics and Statisticsen_US
dc.degree.grantorUniversity of Guelphen_US
dc.degree.nameMaster of Scienceen_US
dc.description.abstractCompletely positive linear maps between 'C'*-algebras were originally developed in the 1950's as a special case of positive linear operators between matrix algebras. Within the last two decades, mathematical physicists have determined that completely positive maps play a crucial role in quantum information theory as structures which model information transfer between quantum systems. In this thesis we analyze two main classes of completely positive linear maps: the Schur maps which arise from the Schur matrix product and maps which are equal to their adjoint. In the analysis of Schur maps, we prove that many of the geometric properties of the convex set of correlation matrices may be derived from analysis of the set of Schur maps We then give several necessary and sufficient conditions on characterizing self-dual completely positive linear maps. In doing so, we completely characterize the extreme points of the convex set of 2 * 2 unital self-dual completely positive trace-preserving linear maps. Finally, we use the concept of a conditional expectation to provide a general framework for some of the special classes of completely positive linear maps.en_US
dc.identifier.urihttps://hdl.handle.net/10214/22485
dc.language.isoen
dc.publisherUniversity of Guelphen_US
dc.rights.licenseAll items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated.
dc.subjectcompletely positive linear mapsen_US
dc.subjectmatrix algebraen_US
dc.subjectquantum information theoryen_US
dc.subjectSchur mapsen_US
dc.subjectself-dualen_US
dc.titleSpecial classes of completely positive linear mapsen_US
dc.typeThesisen_US

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