An Operational Road towards Understanding Causal Indefiniteness within Post-Quantum Theories
MetadataShow full item record
A 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.
Cite this version of the work
Nitica Sakharwade (2022). An Operational Road towards Understanding Causal Indefiniteness within Post-Quantum Theories. UWSpace. http://hdl.handle.net/10012/17841
Showing items related by title, author, creator and subject.
Corona Ugalde, Paulina (University of Waterloo, 2017-09-21)This thesis is concerned with advancing the confrontation between relativistic quantum information (RQI) and experiment. We investigate the lessons that some present-day experiments can teach us about the relationship ...
Bab Hadiashar, Shima (University of Waterloo, 2020-12-21)This thesis consists of two parts: quantum compression and quantum learning theory. A common theme between these problems is that we study them through the lens of information theory. We first study the task of visible ...
Topics on the information theoretic limits of quantum information processing and its implementation Raeisi, Sadegh (University of Waterloo, 2015-02-24)Recent advances in quantum technologies enabled us to make large quantum states and pushed towards examining quantum theory at the macroscopic level. However observation of quantum e ects at a macroscopic level still ...