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dc.contributor.advisorSanders, Barry C.
dc.contributor.authorDhand, Ish
dc.date.accessioned2015-12-15T16:00:19Z
dc.date.available2015-12-15T16:00:19Z
dc.date.issued2015-12-15
dc.date.submitted2015en
dc.identifier.citationDhand, I. (2015). Multi-Photon Multi-Channel Interferometry for Quantum Information Processing (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/27032en_US
dc.identifier.urihttp://hdl.handle.net/11023/2673
dc.description.abstractThis thesis reports advances in the theory of design, characterization and simulation of multi- photon multi-channel interferometers. I advance the design of interferometers through an algorithm to realize an arbitrary discrete unitary transformation on the combined spatial and internal degrees of freedom of light. This procedure effects an arbitrary n_s n_p × n_s n_p unitary matrix on the state of light in n_s spatial and n_p internal modes. The number of beam splitters required to realize a unitary transformation is reduced as compared to existing realization by a factor n_p^2/2. I thus enable the optical implementation of higher dimensional unitary transformations. I devise an accurate and precise procedure for characterizing any multi-port linear optical interferometer using one- and two-photon interference. Accuracy is achieved by estimating and correcting systematic errors that arise due to spatiotemporal and polarization mode mismatch. Enhanced accuracy and precision are attained by fitting experimental coincidence data to a curve simulated using measured source spectra. The efficacy of our characterization procedure is verified by numerical simulations. I develop group-theoretic methods for the analysis and simulation of linear interferometers. I devise a graph-theoretic algorithm to construct the boson realizations of the canonical SU(n) basis states, which reduce the canonical subgroup chain, for arbitrary n. The boson realizations are employed to construct D-functions, which are the matrix elements of arbitrary irreducible representations, of SU(n) in the canonical basis. I show that immanants of principal submatrices of a unitary matrix T are a sum Σ_tD^{(λ)}_{tt}(Ω) of the diagonal D-functions of group element Ω, with t determined by the choice of submatrix, and the irrep (λ) determined by the immanant under consideration. The algorithm for SU(n) D-function computation and the results connecting these functions with immanants open the possibility of group-theoretic analysis and simulation of linear optics.en_US
dc.language.isoeng
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectOptics
dc.subjectPhysics--Theory
dc.subject.classificationLinear Opticsen_US
dc.subject.classificationMultiphoton interferometryen_US
dc.subject.classificationOptical realization of unitary tranformationsen_US
dc.subject.classificationAccurate and precise characterization of linear opticsen_US
dc.subject.classificationGroup theory of multiphoton interferometryen_US
dc.titleMulti-Photon Multi-Channel Interferometry for Quantum Information Processing
dc.typedoctoral thesis
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgaryen
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/27032
thesis.degree.nameDoctor of Philosophy
thesis.degree.namePhD
thesis.degree.disciplinePhysics and Astronomy
thesis.degree.grantorUniversity of Calgary
atmire.migration.oldid3912
dc.contributor.committeememberBartlett, Stephen
dc.contributor.committeememberKusalik, Peter
dc.contributor.committeememberHobill, David
dc.contributor.committeememberLvovsky, Alexander
dc.publisher.placeCalgaryen


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