  Investigating a class of models that is familiar in studies of cellular
automata, we find that quantum operators can be employed to describe their long
distance behavior. These operators span a Hilbert space that appears to turn
such a model into a genuine quantum field theory, obeying the usual conditions
of locality in terms of its quantum commutators. Entangled states can be
constructed exactly as in quantum theories.
  This raises the question whether such models allow Bell's inequalities to be
violated. Being a local, deterministic theory, one would argue that this is
impossible, but since at large distance scales the model does not seem to
differ from real quantum field theories, there is reason to wonder why it
should not allow entangled states. The standard arguments concerning Bell's
inequalities are re-examined in this light.
