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We provide the sandwiched R\'enyi divergence of order$\alpha\in(\frac{1}{2},1)$, as well as its induced quantum informationquantities, with an operational interpretation in the characterization of theexact strong converse exponents of quantum tasks. Specifically, we consider (a)smoothing of the max-relative entropy, (b) quantum privacy amplification, and(c) quantum information decoupling. We solve the problem of determining theexact strong converse exponents for these three tasks, with the performancebeing measured by the fidelity or purified distance. The results are given interms of the sandwiched R\'enyi divergence of order $\alpha\in(\frac{1}{2},1)$,and its induced quantum R\'enyi conditional entropy and quantum R\'enyi mutualinformation. This is the first time to find the precise operational meaning forthe sandwiched R\'enyi divergence with R\'enyi parameter in the interval$\alpha\in(\frac{1}{2},1)$.

Operational Interpretation of the Sandwiched R\'enyi Divergence of Order 1/2 to 1 as Strong Converse Exponents