Reversibility and quantum coherence in one-dimensional quantum cellular automata

Quantum cellular automata are important tools in understanding quantum dynamics, thanks to their simple and effective list of rules. Here we consider a class of noisy, one-dimensional quantum cellular automata that allow one to shift from unitary dynamics to completely positive maps, investigating the evolution of coherence as well as the notion of reversibility in such a setting. To this aim, we associate an approximate reverse automaton to each noisy automaton, and assess its effect, and we define an irreversibility time based on the distance from the maximally mixed state, which is shown to be the only attractor of the automaton map in the presence of dephasing. Our analysis illustrates the interplay between unitary and noisy dynamics.