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：我们为α∈(1/2,1)的序贯Rényi散度及其诱导的量子信息量提供了操作解释，用于刻画量子任务的精确强逆指数。具体而言，我们考虑以下任务：(a)最大相对熵的平滑化，(b)量子隐私放大，以及(c)量子信息解耦。我们解决了确定这三个任务的精确强逆指数的问题，其中性能通过保真度或纯化距离度量。结果以α∈(1/2,1)的序贯Rényi散度及其诱导的量子Rényi条件熵与量子Rényi互信息表示。这是首次为Rényi参数在α∈(1/2,1)区间内的序贯Rényi散度找到精确的操作意义。