Does causal dynamics imply local interactions?

Understand

We consider quantum systems with causal dynamics in discrete spacetimes, also known as quantum cellular automata (QCA).

• Due to time-discreteness this type of dynamics is not characterized by a Hamiltonian but by a one-time-step unitary.
• This can be written as the exponential of a Hamiltonian but in a highly non-unique way.
• We ask if any of the Hamiltonians generating a QCA unitary is local in some sense, and we obtain two very different answers.