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dc.contributor.advisorYang, Wei-Shih
dc.creatorLagro, Matthew Patrick
dc.date.accessioned2020-11-04T16:09:59Z
dc.date.available2020-11-04T16:09:59Z
dc.date.issued2015
dc.identifier.other958157493
dc.identifier.urihttp://hdl.handle.net/20.500.12613/3157
dc.description.abstractQuantum random walks are a generalization of classical Markovian random walks to a quantum mechanical or quantum computing setting. Quantum walks have promising applications but are complicated by quantum decoherence. We prove that the long-time limiting behavior of the class of quantum operations which are the convex combination of norm one operators is governed by the eigenvectors with norm one eigenvalues which are shared by the operators. This class includes all operations formed by a coherent operation with positive probability of orthogonal measurement at each step. We also prove that any operation that has range contained in a low enough dimension subspace of the space of density operators has limiting behavior isomorphic to an associated Markov chain. A particular class of such operations are coherent operations followed by an orthogonal measurement. Applications of the convergence theorems to quantum walks are given.
dc.format.extent54 pages
dc.language.isoeng
dc.publisherTemple University. Libraries
dc.relation.ispartofTheses and Dissertations
dc.rightsIN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available.
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectMathematics
dc.subjectLinear Algebra
dc.subjectProbability
dc.subjectQuantum Operations
dc.subjectQuantum Random Walks
dc.subjectQuantum Walks
dc.titleA Perron-Frobenius Type of Theorem for Quantum Operations
dc.typeText
dc.type.genreThesis/Dissertation
dc.contributor.committeememberSzyld, Daniel
dc.contributor.committeememberRider, Brian
dc.contributor.committeememberTan, Chiu C.
dc.description.departmentMathematics
dc.relation.doihttp://dx.doi.org/10.34944/dspace/3139
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.description.degreePh.D.
refterms.dateFOA2020-11-04T16:09:59Z


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