Capacity Formulas for the Lossy Bosonic Compound Wiretap Channel

We consider the bosonic compound wiretap channel. A pair of lossy channels connects a sender with both a (legitimate) receiver and an eavesdropper. The sender and receiver have only partial information about the actual state of the channels. In this situation, their task is to transmit the maximum amount of messages over an asymptotically large number of uses of their channel while guaranteeing at the same time that only an (asymptotically) negligible amount of information leaks to the eavesdropper. We prove capacity formulas for the case where both sender and receiver have the same information about the system and for the case where the sender has channel state information.