Quantum Homogenization in Permanently Coupled Systems

　Homogenization protocols model the quantum mechanical evolution of asystem into a fixed state independently from the initial configurationof the system by repeatedly coupling it with a collection of identicallyprepared controller ancillas.
　Here we analyze these protocols within the formalism of "relaxing"channels providing an easy to check sufficient condition for homogenization.
　In this context we describe full homogenization schemes which allow usto derive the relaxation to a fixed state in a network of connectedqudits by only interacting with few of them. Furthermore, we studyconfigurations which allow us to introduce entanglement among theelements of a network.