Multi-Mode Multi-Photon Interferometry Applications for Quantum Information Processing

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dc.contributor.advisorSanders, Barry C.
dc.contributor.authorKhalid, Abdullah
dc.contributor.committeememberBarclay, Paul E.
dc.contributor.committeememberGour, Gilad
dc.contributor.committeememberSafavi-Naini, Reihaneh S.
dc.contributor.committeememberSánchez-Soto, Luis L.
dc.date2018-11
dc.date.accessioned2018-10-02T18:09:56Z
dc.date.available2018-10-02T18:09:56Z
dc.date.issued2018-09-21
dc.description.abstractQuantum information holds enormous potential to achieve communication and computational tasks that are impossible using classical systems. Many quantum information processing tasks can be implemented by exploiting the passive interference of photons. In this thesis, we reports advances towards the analysis, simulation, characterization, and design of passive interferometry experiments for quantum information processing applications. First, we develop a theory of passive optical interferometry experiments that relates coincidence rates at the output of an interferometer to the permutational symmetries of partially distinguishable photons. In our formalism, coincidence rates are elegantly expressed in terms of immanants, which are matrix functions that exhibit permutational symmetries, and the immanants appearing in our coincidence-rate expressions share permutational symmetries with the input state. Our formalism thus provides an intuitive qualitative understanding of how the permutational symmetries of distinguishable photons determine their interference. Our approach can be used to better understand the effect of partial distinguishability in modeling passive interferometry experiments aiming to perform quantum information tasks such as linear optical quantum computing and BosonSampling. By exploiting symmetries, we can also reduce some calculational tasks and provide additional insights into relations between the coincidence rates in various situations. Second, we tackle the problem of characterizing passive interferometers, essential for modelling any passive interferometry experiment. We develop a characterization procedure that uses only one- and two-photon coincidence data, and makes a number of advancements over existing procedures. We estimate the errors in the characterization via bootstrapping, a statistical technique with the advantage of not assuming any particular error model on the experimental data. We also introduce a scattershot approach to reduce the experimental data collection time quadratically in the number of modes of the interferometer. Third, we study a relativistic quantum information task called quantum summoning. We cast quantum summoning as an interactive protocol between a verifier and a possibly dishonest prover. For the prover, we present a protocol and quantum codes to summon in any valid configuration of causal diamonds, and design the encoding and decoding circuits for our code. Our protocol decreases the space complexity for encoding by a factor of two compared to the previous best result and reduces the gate complexity from scaling as the cube to the square of the number of causal diamonds. Within our interactive protocol framework, we construct an operational definition of quantum summoning, and use this definition to present a verification test. We prove that our verification test is sound and complete, thereby showing that quantum summoning can be verified by a resource-limited verifier in an adversarial setting. Our protocol and verification procedures are amenable to implementation by passive interferometry, thereby extending the reach of passive interferometry in the field of relativistic quantum information processing.en_US
dc.identifier.citationKhalid, A. (2018). Multi-Mode Multi-Photon Interferometry Applications for Quantum Information Processing (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/33073en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/33073
dc.identifier.urihttp://hdl.handle.net/1880/108720
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.facultyScience
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
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.subjectQuantum information
dc.subjectQuantum optics
dc.subjectPassive interferometry
dc.subject.classificationPhysicsen_US
dc.subject.classificationOpticsen_US
dc.titleMulti-Mode Multi-Photon Interferometry Applications for Quantum Information Processing
dc.typedoctoral thesis
thesis.degree.disciplinePhysics and Astronomy
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameDoctor of Philosophy (PhD)
ucalgary.item.requestcopytrue
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