Quaternions and Quantum Theory

dc.contributor.authorGraydon, Matthew
dc.date.accessioned2011-08-30T16:01:45Z
dc.date.available2011-08-30T16:01:45Z
dc.date.issued2011-08-30T16:01:45Z
dc.date.submitted2011-08-05
dc.description.abstractThe orthodox formulation of quantum theory invokes the mathematical apparatus of complex Hilbert space. In this thesis, we consider a quaternionic quantum formalism for the description of quantum states, quantum channels, and quantum measurements. We prove that probabilities for outcomes of quaternionic quantum measurements arise from canonical inner products of the corresponding quaternionic quantum effects and a unique quaternionic quantum state. We embed quaternionic quantum theory into the framework of usual complex quantum information theory. We prove that quaternionic quantum measurements can be simulated by usual complex positive operator valued measures. Furthermore, we prove that quaternionic quantum channels can be simulated by completely positive trace preserving maps on complex quantum states. We also derive a lower bound on an orthonormality measure for sets of positive semi-definite quaternionic linear operators. We prove that sets of operators saturating the aforementioned lower bound facilitate a reconciliation of quaternionic quantum theory with a generalized Quantum Bayesian framework for reconstructing quantum state spaces.en
dc.identifier.urihttp://hdl.handle.net/10012/6168
dc.language.isoenen
dc.pendingfalseen
dc.publisherUniversity of Waterlooen
dc.subjectquantumen
dc.subjectquaternionicen
dc.subject.programPhysicsen
dc.titleQuaternions and Quantum Theoryen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Scienceen
uws-etd.degree.departmentPhysics and Astronomyen
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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