  We determine the exact strong converse exponent for entanglement-assisted
classical communication of a quantum channel. Our main contribution is the
derivation of an upper bound for the strong converse exponent which is
characterized by the sandwiched R\'enyi divergence. It turns out that this
upper bound coincides with the lower bound of Gupta and Wilde (Commun. Math.
Phys. 334:867-887, 2015). Thus, the strong converse exponent follows from the
combination of these two bounds. Our result has two implications. Firstly, it
implies that the exponential bound for the strong converse property of
quantum-feedback-assisted classical communication, derived by Cooney, Mosonyi
and Wilde (Commun. Math. Phys. 344:797-829, 2016), is optimal. This answers
their open question in the affirmative. Hence, we have determined the exact
strong converse exponent for this problem as well. Secondly, due to an
observation of Leung and Matthews, it can be easily extended to deal with the
transmission of quantum information under the assistance of entanglement or
quantum feedback, yielding similar results. The above findings provide, for the
first time, a complete operational interpretation to the channel's sandwiched
R\'enyi information of order $\alpha > 1$.
