We provide the sandwiched R\'enyi divergence of order $\alpha\in(\frac{1}{2},1)$, as well as its induced quantum information quantities, with an operational interpretation in the characterization of the exact 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 the exact strong converse exponents for these three tasks, with the performance being measured by the fidelity or purified distance. The results are given in terms 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 mutual information. This is the first time to find the precise operational meaning for the sandwiched R\'enyi divergence with R\'enyi parameter in the interval $\alpha\in(\frac{1}{2},1)$.

翻译：我们给出了阶数$\alpha\in(\frac{1}{2},1)$的Sandwiched Rényi散度及其诱导的量子信息量在刻画量子任务精确强逆指数中的操作诠释。具体地，我们考虑了(a)最大相对熵的光滑化、(b)量子隐私放大以及(c)量子信息解耦这三个任务。我们解决了确定这些任务精确强逆指数的问题，其中性能通过保真度或纯化距离来度量。结果以阶数$\alpha\in(\frac{1}{2},1)$的Sandwiched Rényi散度及其诱导的量子Rényi条件熵和量子Rényi互信息的形式给出。这是首次为Rényi参数位于区间$\alpha\in(\frac{1}{2},1)$内的Sandwiched Rényi散度找到精确的操作意义。