In my talk I will present some probability properties for quantum channels, and I will show some similarities with the theory of classical Markov chains. At first I will introduce the concepts of reducibility,  invariant state and enclosure. After that I will discuss the structure of invariant states related to the possible decompositions in enclosures of the positive recurrent subspace. Finally I will reconsider this result for a particular case of homogeneous open quantum random walks. 

This talk is based on the contents of my Master's thesis (Tesi di Laurea Magistrale).