Quantum communication under channel uncertainty

This work contains results concerning transmission of entanglement and subspaces as well as generation of entanglement in the limit of arbitrary many uses of compound- and arbitrarily varying quantum channels (CQC, AVQC). In both cases, the channel is described by a set of memoryless channels. Only forward communication between one sender and one receiver is allowed. A code is said to be ''good'' only, if it is ''good'' for every channel out of the set. Both settings describe a scenario, in which sender and receiver have only limited channel knowledge. For different amounts of information about the channel available to sender or receiver, coding theorems are proven for the CQC. For the AVQC, both deterministic and randomised coding schemes are considered. Coding theorems are proven, as well as a quantum analogue of the Ahlswede-dichotomy. The connection to zero-error capacities of stationary memoryless quantum channels is investigated. The notion of symmetrisability is defined and used for both classes of channels.