Coding theorems for quantum communication channels

The more than thirty years old issue of the information capacity of quantum communication channels was dramatically clarified during when a number of direct quantum coding theorems were discovered. To a considerable extent this progress is due to an interplay between the quantum communication theory and quantum information ideas related to more recent development in quantum computing. It is remarkable, however, that many probabilistic tools underlying the treatment of the quantum case have their roots, and in some cases direct prototypes, in the classical Shannon theory.