论文标题
量子相对熵的收敛条件和未命名量子dini引理的其他应用
Convergence conditions for the quantum relative entropy and other applications of the deneralized quantum Dini lemma
论文作者
论文摘要
我们描述了该结果的广义版本称为量子DINI引理，该版本以前用于分析基本相关和纠缠措施的局部连续性。概括在于考虑函数序列而不是单个函数。它使我们能够扩大该方法可能应用的范围。我们证明了两个普遍主导的融合定理和关于在凸混合物下保持局部连续性的定理。 通过使用这些定理，我们获得了量子相对熵的几个收敛条件以及被认为是对的函数（通道，输入状态）的量子通道的互信息。还获得了Von Neumann熵的简单收敛标准。
We describe a generalized version of the result called quantum Dini lemma that was used previously for analysis of local continuity of basic correlation and entanglement measures. The generalization consists in considering sequences of functions instead of a single function. It allows us to expand the scope of possible applications of the method. We prove two general dominated convergence theorems and the theorem about preserving local continuity under convex mixtures. By using these theorems we obtain several convergence conditions for the quantum relative entropy and for the mutual information of a quantum channel considered as a function of a pair (channel, input state). A simple convergence criterion for the von Neumann entropy is also obtained.
