Abstract

It is shown that the recently established lower semicontinuity of the quantum conditional mutual information implies (in fact, is equivalent to) the lower semicontinuity of the loss of the quantum (conditional) mutual information under local channels considered as a function on the Cartesian product of the set of all states of a composite system and the sets of all local channels (equipped with the strong convergence topology). Some applications of this property are considered. New continuity conditions for the quantum mutual information and for the squashed entanglement in both bipartite and multipartite infinite-dimensional systems are obtained. It is proved, in particular, that the multipartite squashed entanglement of any countably indecomposable separable state with finite marginal entropies is equal to zero. Special continuity properties of the information gain of a quantum measurement with and without quantum side information are established that can be treated as robustness (stability) of these quantities with respect to perturbation of the measurement and the measured state.

中文翻译：

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量子条件互信息的下半连续性及其推论

摘要

结果表明，最近建立的量子条件互信息的下半连续性意味着（实际上，等价于）局部信道下量子（条件）互信息丢失的下半连续性，被认为是笛卡尔积的函数复合系统所有状态的集合和所有本地通道的集合（配备强收敛拓扑）。考虑了该特性的一些应用。获得了二分和多分无限维系统中量子互信息和压缩纠缠的新连续性条件。特别是，证明了具有有限边际熵的任何可数不可分解可分离状态的多部分压缩纠缠等于 0。