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The fully quantum reverse Shannon theorem establishes the optimal rate ofnoiseless classical communication required for simulating the action of manyinstances of a noisy quantum channel on an arbitrary input state, while alsoallowing for an arbitrary amount of shared entanglement of an arbitrary form.Turning this theorem around establishes a strong converse for theentanglement-assisted classical capacity of any quantum channel. This paperproves the strong converse for entanglement-assisted capacity by a completelydifferent approach and identifies a bound on the strong converse exponent forthis task. Namely, we exploit the recent entanglement-assisted "meta-converse"theorem of Matthews and Wehner, several properties of the recently establishedsandwiched Renyi relative entropy (also referred to as the quantum Renyidivergence), and the multiplicativity of completely bounded $p$-norms due toDevetak et al. The proof here demonstrates the extent to which the Arimotoapproach can be helpful in proving strong converse theorems, it provides anoperational relevance for the multiplicativity result of Devetak et al., and itadds to the growing body of evidence that the sandwiched Renyi relative entropyis the correct quantum generalization of the classical concept for all$\alpha>1$.

Multiplicativity of completely bounded $p$-norms implies a strong converse for entanglement-assisted capacity