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

Causality and logic are both fundamental to our understanding of the universe, but our intuitions about these are challenged by quantum phenomena. This thesis reports progress in the analysis of causality and multi-agent logical paradoxes in quantum and post-quantum theories. Both these research areas are highly relevant for the development of quantum technologies such as quantum cryptography and computing.

Part I of this thesis focuses on causality. Firstly, we develop techniques for using generalised entropies
to analyse distinctions between classical and non-classical causal structures. We derive new properties of classical and quantum 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. Secondly, 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 Part II of this thesis, we investigate multi-agent logical paradoxes, of which the quantum Frauchiger-Renner paradox has been the only example. We 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, unitary evolution of agents' memories is not necessary for deriving multi-agent logical paradoxes, rather that certain forms of contextuality could be.