Approaches to causality and multi-agent paradoxes in non-classical theories

Abstract: This thesis reports progress in the analysis of causality and multi-agent logical paradoxes in quantum and post-quantum theories. These research areas are highly relevant for the foundations of physics as well as the development of quantum technologies. In the first part, focussing on causality, we develop techniques for using generalised entropies to analyse distinctions between classical and non-classical causal structures. We derive new properties of Tsallis entropies of systems that follow from the relevant causal structure, and apply these to obtain new necessary constraints for classicality in the Triangle causal structure. Supplementing the method with the post-selection technique, we provide evidence that Shannon and Tsallis entropic constraints are insufficient for detecting non-classicality in Bell scenarios with non-binary outcomes. This points to the need for better methods of characterising correlations in non-classical causal structures. Further, we investigate the relationships between causality and space-time by developing a framework for modelling cyclic and fine-tuned influences in non-classical theories. We derive necessary and sufficient conditions for such causal models to be compatible with a space-time structure and for ruling out operationally detectable causal loops. In particular, this provides an operational framework for analysing post-quantum theories admitting jamming non-local correlations. In the second part, we investigate multi-agent logical paradoxes such as the Frauchiger-Renner paradox and develop a framework for analysing such paradoxes in arbitrary physical theories. Applying this to box world, a post-quantum theory, we derive a stronger paradox that does not rely on post-selection. Our results reveal that reversible evolution of agents' memories is not necessary for deriving multi-agent paradoxes, and that certain forms of contextuality might be.