Time symmetry in quantum theories and beyond

There exists a stark tension among different formulations of quantum theory as some are inherently time-symmetric while others are time-asymmetric. This tension is crisply captured when considering physical theories as theories of processes. We present the process theory of quantum physics, QPhys, which treats classical systems as internal to quantum theory. We provide three ways to incorporate time symmetry in QPhys. The first restricts the process theory of QPhys to one that satisfies an additional retrocausality constraint. The second is a novel approach, which extends the notions of causality and retrocausality to apply to systems along with processes. Utilizing this approach, we create a toy model for particle physics , where the causal and retrocausal systems correspond to particles and anti-particles respectively. The third approach extends QPhys to a supertheory that satisfies neither a causality nor a retrocausality constraint. To avoid unphysical predictions we modify either its composition rule or its processes.