  A fully general strong converse for channel coding states that when the rate
of sending classical information exceeds the capacity of a quantum channel, the
probability of correctly decoding goes to zero exponentially in the number of
channel uses, even when we allow code states which are entangled across several
uses of the channel. Such a statement was previously only known for classical
channels and the quantum identity channel. By relating the problem to the
additivity of minimum output entropies, we show that a strong converse holds
for a large class of channels, including all unital qubit channels, the
d-dimensional depolarizing channel and the Werner-Holevo channel. This further
justifies the interpretation of the classical capacity as a sharp threshold for
information-transmission.
