It is proved that the decrease of the quantum relative entropy under action of a quantum operation is a lower semicontinuous function of a pair of its arguments. This property implies, in particular, that the local discontinuity jumps of the quantum relative entropy do not increase under action of quantum operations. It implies also the lower semicontinuity of the modulus of the joint convexity of the quantum relative entropy (as a function of ensembles of quantum states). Various corollaries and applications of these results are considered.

翻译：本文证明了量子相对熵在量子操作作用下的递减量是其参数对的弱下半连续函数。这一性质特别意味着量子相对熵的局部不连续跳跃在量子操作作用下不会增加。该性质还蕴含了量子相对熵联合凸性模量的下半连续性（作为量子态系综的函数）。本文进一步探讨了这些结果的若干推论与应用。