An Operational Road towards Understanding Causal Indefiniteness within Post-Quantum Theories

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dc.contributor.authorSakharwade, Nitica
dc.date.accessioned2022-01-07T15:34:49Z
dc.date.available2022-01-07T15:34:49Z
dc.date.issued2022-01-07
dc.date.submitted2021-12-22
dc.description.abstractA theory, whatever it does, must correlate data. We commit ourselves to operational methodology, as a means towards studying the space of Generalised Probability Theories that are compatible with Indefinite Causality. Such a space of theories that combines the radical aspects of Quantum Theory: its probabilistic nature and of Relativity: its dynamic causal structure, is expected to house Quantum Gravity. In this thesis, we ask how we may understand Indefinite Causality. In the first half, we explore the consequences of (Indefinite) Causality on Communication tasks. Motivated by the game with one way signalling that provided the Causal Inequality, we study competing two-way signalling and provide protocols for Bidirectional Teleportation and Bidirectional Dense-Coding. Further, we provide a theorem for when tensor products of processes are valid. This result has consequences for setting up of a theory of process communication. In the second half, we revisit the Causaloid Framework by Hardy, a framework that studies this space of theories and prescribes how to recover the correlations within a theory from operational data to calculate probabilities through three levels of physical compression -- Tomographic, Compositional and Meta. We present a diagrammatic representation for the Causaloid Framework and leverage it to study Meta-Compression through which we characterise a Hierarchy of theories. The rungs of this Hierarchy are differentiated by the nature of the Causal Structure of the theory. We apply the Causaloid Framework to the space of Generalised Probability Theories pertaining to circuits, through the Duotensor Framework and show that finite dimensional Quantum Theory as well as Classical Probability Theory belong to its second rung. To summarise, we work towards a better understanding of communication tasks when the underlying causal structure is indefinite, and characterise the space of Generalised Probability Theories with Indefinite Causality, through the nature of their causal structures.en
dc.identifier.urihttp://hdl.handle.net/10012/17841
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectindefinite causal structureen
dc.subjectquantum foundationsen
dc.subjectoperational methodologyen
dc.subjectpost-quantumen
dc.subjectcommunication protocolen
dc.subjectprocess matrixen
dc.subjectcausaloiden
dc.subjectduotensorsen
dc.subjectquantum communicationen
dc.subjectteleportationen
dc.subjectdense-codingen
dc.subjectquantum informationen
dc.subjectquantum gravityen
dc.subjectquantumen
dc.subjectcausalen
dc.subjectoperationalen
dc.subjectframeworken
dc.subjectbutterfly networken
dc.subjectformalism localityen
dc.subjectformalism localen
dc.titleAn Operational Road towards Understanding Causal Indefiniteness within Post-Quantum Theoriesen
dc.typeDoctoral Thesisen
uws-etd.degreeDoctor of Philosophyen
uws-etd.degree.departmentPhysics and Astronomyen
uws-etd.degree.disciplinePhysicsen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.embargo.terms0en
uws.comment.hiddenDefense was on 14th Dec 2021. Revisions were accepted on 22nd Dec 2021.en
uws.contributor.advisorHardy, Lucien
uws.contributor.advisorKempf, Achim
uws.contributor.affiliation1Faculty of Scienceen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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