Building on established literature and recent developments in the graph-theoretic characterisation of its CPM category, we provide a treatment of pure state and mixed state quantum mechanics in the category fRel of finite sets and relations. On the way, we highlight the wealth of exotic beasts that hide amongst the extensive operational and structural similarities that the theory shares with more traditional arenas of categorical quantum mechanics, such as the category fdHilb. We conclude our journey by proving that fRel is local, but not without some unexpected twists.
- Pub Date:
- June 2015
- Quantum Physics;
- Computer Science - Logic in Computer Science;
- Mathematics - Category Theory;
- Mathematics - Quantum Algebra
- In Proceedings QPL 2015, arXiv:1511.01181