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Entanglement assisted classical capacity of compound quantum channels

We consider the task of entanglement assisted message transmission under presence of a compound memoryless quantum channel. In this model, the completely positive and trace preserving map governing the channel statistics is, instead of being perfectly known, only revealed as member of a certain set of channels. Therefore, coding schemes have to be used which are simultaneously reliable for each member of this set. Utilizing universal codes for classical-quantum channels, we introduce optimal universal coding schemes for entanglement assisted message transmission of compound quantum channels. The resulting coding theorem together with a corresponding converse statement leads us to a single-letter expression for the entanglement assisted message transmission capacity of compound quantum channels.