Show simple item record

dc.contributor.authorGraydon, Matthew 16:01:45 (GMT) 16:01:45 (GMT)
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.publisherUniversity of Waterlooen
dc.titleQuaternions and Quantum Theoryen
dc.typeMaster Thesisen
dc.subject.programPhysicsen and Astronomyen
uws-etd.degreeMaster of Scienceen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages