In the problem of binary quantum channel discrimination with product inputs, the supremum of all type II error exponents for which the optimal type I errors go to zero is equal to the Umegaki channel relative entropy, while the infimum of all type II error exponents for which the optimal type I errors go to one is equal to the infimum of the sandwiched channel R\'enyi $\alpha$-divergences over all $\alpha>1$. We prove the equality of these two threshold values (and therefore the strong converse property for this problem) using a minimax argument based on a newly established continuity property of the sandwiched R\'enyi divergences. Motivated by this, we give a detailed analysis of the continuity properties of various other quantum (channel) R\'enyi divergences, which may be of independent interest.

翻译：在乘积输入的二元量子信道辨别问题中，使得最优第一类错误趋于零的所有第二类错误指数的上确界等于Umegaki信道相对熵，而使得最优第一类错误趋于一的所有第二类错误指数的下确界等于所有α>1下的夹层信道Rényi α-散度的下确界。我们基于新建立的夹层Rényi散度的连续性性质，通过极小化极大论证证明了这两个阈值相等（从而该问题具有强对偶性）。受此启发，我们详细分析了其他多种量子（信道）Rényi散度的连续性性质，这些结果可能具有独立的研究价值。