Generating quantum dynamic mapping

We consider one-parameter families of generating quantum channels. Such families are called the generating quantum dynamical mapping or the generating quantum processes. By the generating channels of composite quantum systems, we understand the channels that allow the channels of constituent subsystems, called the generated channels, to be uniquely defined. Using the criterion for generating and generated linear mappings, we study the properties of bijective quantum channels and the properties of quantum processes consisting of such channels. Using the generating quantum dynamical mapping, we naturally construct the generated dynamical mapping. We show that the properties of continuity and completely positive divisibility of generating quantum dynamical mappings are hereditary for generated dynamical mappings. As an application of the obtained results, we construct continuous completely positive evolutions. For generating quantum dynamical mappings taking values in the set of phase-damping channels, we obtain a criterion for the completely positive divisibility.