Open quantum walks

Quantum walks, i.e., quantum evolution of a particle moving on some underlying graph structure, play an important role in quantum information theory. The system is said to be open if it interacts with its environment, i.e., the evolution loses information and is therefore nonreversible. In this sense, open quantum walks can be considered as quantum analogs of Markov chains. We will give an introduction to open quantum walks in the context of operator algebras and look at some examples coming from Cayley graphs of monoids.