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A strong converse theorem for the classical capacity of a quantum channelstates that the probability of correctly decoding a classical message convergesexponentially fast to zero in the limit of many channel uses if the rate ofcommunication exceeds the classical capacity of the channel. Along with acorresponding achievability statement for rates below the capacity, such astrong converse theorem enhances our understanding of the capacity as a verysharp dividing line between achievable and unachievable rates of communication.Here, we show that such a strong converse theorem holds for the classicalcapacity of all entanglement-breaking channels and all Hadamard channels (thecomplementary channels of the former). These results follow by bounding thesuccess probability in terms of a "sandwiched" Renyi relative entropy, byshowing that this quantity is subadditive for all entanglement-breaking andHadamard channels, and by relating this quantity to the Holevo capacity. Priorresults regarding strong converse theorems for particular covariant channelsemerge as a special case of our results.

Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy