  A strong converse theorem for the classical capacity of a quantum channel
states that the probability of correctly decoding a classical message converges
exponentially fast to zero in the limit of many channel uses if the rate of
communication exceeds the classical capacity of the channel. Along with a
corresponding achievability statement for rates below the capacity, such a
strong converse theorem enhances our understanding of the capacity as a very
sharp dividing line between achievable and unachievable rates of communication.
Here, we show that such a strong converse theorem holds for the classical
capacity of all entanglement-breaking channels and all Hadamard channels (the
complementary channels of the former). These results follow by bounding the
success probability in terms of a "sandwiched" Renyi relative entropy, by
showing that this quantity is subadditive for all entanglement-breaking and
Hadamard channels, and by relating this quantity to the Holevo capacity. Prior
results regarding strong converse theorems for particular covariant channels
emerge as a special case of our results.
