  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.
