The uncertainty principle determines the distinction between the classical and the quantum world. This principle states that it is not possible to measure two incompatible observables with the desired accuracy simultaneously. In quantum information theory, the Shannon entropy is used as an appropriate measure to express the uncertainty relation. Improving the bound of the entropic uncertainty relation is of great importance. The bound can be varied by considering an extra quantum system as the quantum memory which is correlated with the measured quantum system. One can extend the bipartite quantum-memory-assisted entropic uncertainty relation to the tripartite one in which the memory is split into two parts. Here, a lower bound is obtained for the tripartite quantum-memory-assisted entropic uncertainty relation. This lower bound has two extra terms compared with the lower bound in Renes and Boileau [J. M. Renes and J.-C. Boileau, Phys. Rev. Lett. 110, 020402 (2013)] which depends on the conditional von Neumann entropy, the Holevo quantity, and the mutual information. It is shown that the bound is tighter than other bounds derived earlier. It also leads to a lower bound for the quantum secret key rate. In addition, it is applied to obtain the states for which both the strong subadditivity and the Koashi-Winter inequalities turn into equalities.

中文翻译：

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加强三方量子记忆辅助的熵不确定性关系

不确定性原则决定了经典世界与量子世界之间的区别。该原理指出，不可能同时以所需的精度测量两个不兼容的可观测物体。在量子信息论中，香农熵被用作表达不确定性关系的一种适当方法。改善熵不确定性关系的边界非常重要。可以通过考虑额外的量子系统作为与测量的量子系统相关的量子存储器来改变边界。一个可以将二元量子记忆辅助的熵不确定性关系扩展到将内存分为两部分的三方。在此，获得了三方量子记忆辅助的熵不确定性关系的下界。与Renes和Boileau的下限相比，此下限有两个额外的术语[JM Renes和J.-C。Boileau，物理 牧师 110，020402（2013）]，它取决于条件冯·诺依曼熵，该Holevo量和互信息。结果表明，该边界比以前导出的其他边界更严格。这也导致了量子秘密密钥率的下限。另外，它被用于获得强次可加性和Koashi-Winter不等式都变为相等的状态。