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：本文为阶数$\alpha\in(\frac{1}{2},1)$的夹逼Rényi散度及其诱导的量子信息量提供了运算诠释，将其表征为量子任务精确强逆指数。具体而言，我们考虑以下三类任务：(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。我们求解了这三类任务精确强逆指数的确定问题，其中性能由保真度或纯化距离度量。结果以阶数$\alpha\in(\frac{1}{2},1)$的夹逼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$\alpha\in(\frac{1}{2},1)$的夹逼Rényi散度找到精确的运算意义。