Fine-Grained Quantum Uncertainty Relations

dc.contributor.advisorGour, Gilad
dc.contributor.authorPoostindouz, Alireza
dc.contributor.committeememberHøyer, Peter
dc.contributor.committeememberSanders, Barry
dc.description.abstractQuantum theory predicts an inherent joint unpredictability for some pairs of measurements. For example, Heisenberg showed that the more precisely the position of a quantum particle is known, the less precisely its momentum can be known and vice versa. Uncertainty relations (URs) are mathematical expressions quantifying the constraints between the output probability distributions of the given sets of measurements. Typically, URs are expressed in terms of uncertainty quantifiers such as entropies. Based on an information-theoretic approach, we discovered a characterization that unifies all uncertainty quantifiers and thus, generalizes a large class of URs into a single framework. We also prove new URs that are fundamentally different from typical URs in that they are fine-grained; i.e. they set restrictions directly on the output probability distributions without using any particular uncertainty quantifiers. We used Majorization theory and other techniques such as matrix analysis to prove our fine-grained uncertainty relations.en_US
dc.identifier.citationPoostindouz, A. (2016). Fine-Grained Quantum Uncertainty Relations (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from doi:10.11575/PRISM/26179en_US
dc.publisher.facultyGraduate Studies
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.
dc.subject.classificationHeisenberg 's Uncertainty Principleen_US
dc.subject.classificationQuantum Measurementsen_US
dc.subject.classificationUncertainty Relationsen_US
dc.subject.classificationInformation Theoryen_US
dc.titleFine-Grained Quantum Uncertainty Relations
dc.typemaster thesis and Astronomy of Calgary of Science (MSc)