Conic Linear Programming in Quantum Information

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dc.contributor.advisorGour, Gilad
dc.contributor.advisorScandolo, Carlo Maria
dc.contributor.authorZafar, Fasiha Binat
dc.contributor.committeememberSanders, Barry C.
dc.contributor.committeememberBarclay, Paul
dc.date2022-02
dc.date.accessioned2022-01-18T16:50:50Z
dc.date.available2022-01-18T16:50:50Z
dc.date.issued2022-01
dc.description.abstractA frequently studied problem in quantum resource theories (QRTs) is converting one resource state into another by applying free operations. If convexity arises in QRTs, convex analysis tools can be utilized in the analysis of these problems. The separating hyperplane theorem ensures the existence of at least one witness for each resource state in convex QRTs. By using this idea, necessary and sufficient conditions in terms of resource monotones are derived for generic convex static QRTs. We use this result to derive the complete family of conversion resource monotones for majorization as a subset of f-divergences. For classical conditional majorization, necessary and sufficient conditions for state conversion are derived in the form of a homogeneous convex function. We unified the pre-existing results under the umbrella of the resource-theoretic framework. The new approach helps in the significant simplification of the proofs. Furthermore, we extend the work to derive a new complete family of conversion monotones for quantum conditional majorization in terms of min-entropy using the same techniques and procedures. We expect the quantum conditional majorization will find operational applications in future work similar to its classical counterpart.en_US
dc.identifier.citationZafar, F. B. (2022). Conic linear programming in quantum information (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/39523
dc.identifier.urihttp://hdl.handle.net/1880/114308
dc.language.isoengen_US
dc.publisher.facultyScienceen_US
dc.publisher.institutionUniversity of Calgaryen
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.en_US
dc.subjectQuantum Informationen_US
dc.subjectResource Theoryen_US
dc.subjectConic Linear Programmingen_US
dc.subject.classificationInformation Scienceen_US
dc.subject.classificationEducation--Mathematicsen_US
dc.subject.classificationEconomics--Theoryen_US
dc.titleConic Linear Programming in Quantum Informationen_US
dc.typemaster thesisen_US
thesis.degree.disciplineMathematics & Statisticsen_US
thesis.degree.grantorUniversity of Calgaryen_US
thesis.degree.nameMaster of Science (MSc)en_US
ucalgary.item.requestcopytrueen_US
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