  Quantum Cellular Automata are unitary maps that preserve locality and respect
causality. We identify them, in any dimension, with simple tensor networks
(PEPU) whose bond dimension does not grow with the system size. As a result,
they satisfy an area law for the entanglement entropy they can create. We
define other classes of non-unitary maps, the so-called quantum channels, that
either respect causality or preserve locality. We show that, whereas the latter
obey an area law for the amount of quantum correlations they can create, as
measured by the quantum mutual information, the former may violate it. We also
show that neither of them can be expressed as tensor networks with a bond
dimension that is independent of the system size.
