Asymptotic Completeness of Quantum Markov Processes

Quantum Markov processes can be obtained from the quantized version of a road-coloured graph. This allows to bring in ideas from coding theory as well as from scattering theory. In particular, asymptotic completeness of a Markov process is closely related to the possibility of preparing states of an open system by prepararing its input states but it also allows a certain coding of the Markov process.

In this talk we give an overview over recent developments in this area. We discuss asymptotic completeness under topological and measure theoretical aspects, present new criteria for asymptotic completeness, which, in particular, cover the micro-maser system, and put asymptotic completeness into the context of coding theory.