Secrecy capacities of compound quantum wiretap channels and applications

We determine the secrecy capacity of the compound channel with quantum wiretapper and channel state information at the transmitter. Moreover, we derive a lower bound on the secrecy capacity of this channel without channel state information and determine the secrecy capacity of the compound classical-quantum wiretap channel with channel state information at the transmitter. We use this result to derive a proof for a lower bound on the entanglement generating capacity of the compound quantum channel. We also derive a proof for the formula for entanglement generating capacity of the compound quantum channel with channel state information at the encoder which was given in additional information [Bjelaković, Boche, and Nötzel, in Proceedings of International Symposium on Information Theory ISIT, Korea, 2009 (IEEE, New York, 2009), pp. 1889-1893].