Unitarity plus causality implies localizability

Understand

We consider a graph with a single quantum system at each node.

• The entire compound system evolves in discrete time steps by iterating a global evolution $U$.
• We require that this global evolution $U$ be unitary, in accordance with quantum theory, and that this global evolution $U$ be causal, in accordance with special relativity.
• By causal we mean that information can only ever be transmitted at a bounded speed, the speed bound being quite naturally that of one edge of the underlying graph per iteration of $U$.