Conference

Cellular automata are a central notion for the formulation of physical laws in an abstract information-theoretical scenario, and lead in recent years to the reconstruction of free relativistic quantum field theory. In this talk we extend the notion of a Quantum Cellular Automaton to general Operational Probabilistic Theories. For this purpose, we construct infinite composite systems, illustrating the main features of their states, effects and transformations. We discuss the generalization of the concepts of homogeneity and locality, in an framework where space-time is not a primitive object. We show that homogeneity leads to a Cayley graph structure of the memory array, thus proving the universality of the connection between homogeneity and discrete groups. We conclude illustrating the special case of Fermionic cellular automata, discussing three relevant examples: Weyl and Dirac quantum walks, the Thirring automaton and the simplest families of automata on finite graphs.