Excitation and entanglement transfer versus spectral gap

We consider quantum many body systems as quantum channels and study the relation between the transfer quality and the size of the spectral gap between the system's ground and excited states. In our setup, two ancillas are weakly coupled to the quantum many body system at different sites, and we study the propagation of an excitation and quantum information from one ancilla to the other. We observe two different scenarios: a slow, but perfect transfer if the gap is large and a fast, but incomplete transfer otherwise. We provide a numerical and analytical approach as well as a simplified physical model explaining our findings. Our results relate the potential of spin chains acting as quantum channels to the concept of quantum phase transitions and offer a different approach to the characterization of these.