论文标题
收紧三方量子记忆辅助熵不确定性关系
Tightening the tripartite quantum memory assisted entropic uncertainty relation
论文作者
论文摘要
不确定性原理决定了古典世界和量子世界之间的区别。该原则指出，不可能同时使用所需的精度测量两个不相容的可观察结果。在量子信息理论中，香农熵已被用作表达不确定性关系的适当措施。根据熵不确定性关系的应用，研究和试图改善这种关系的界限至关重要。不确定性可以通过将额外的量子系统作为量子内存$ b $来改变与测量的量子系统$ a $相关的量子存储器$ b $。一个人可以扩展两分的量子记忆辅助熵不确定性与三方量子记忆的辅助熵不确定性关系，其中存储器分为两部分。在这项工作中，我们获得了三方量子记忆辅助熵不确定性关系的下限。与[Phys的下限相比，我们的下限还有两个额外的术语。莱特牧师。 103，020402（2009）]，这取决于条件von Neumann熵，孔数量和相互信息。结果表明，这项工作中获得的界限比其他边界更紧密。另外，使用我们的下限，已经获得了量子秘密密钥速率的下限。下边界还用于获得强大亚加性不平等和小冬季不平等的状态，对平等满意。
The uncertainty principle determines the distinction between the classical and quantum worlds. This principle states that it is not possible to measure two incompatible observables with the desired accuracy simultaneously. In quantum information theory, Shannon entropy has been used as an appropriate measure to express the uncertainty relation. According to the applications of entropic uncertainty relation, studying and trying to improve the bound of this relation is of great importance. Uncertainty bound can be altered by considering an extra quantum system as the quantum memory $B$ which is correlated with the measured quantum system $A$. One can extend the bipartite quantum memory assisted entropic uncertainty relation to tripartite quantum memory assisted entropic uncertainty relation in which the memory is split into two parts. In this work, we obtain a lower bound for the tripartite quantum memory assisted entropic uncertainty relation. Our lower bound has two additional terms compared to the lower bound in [Phys. Rev. Lett. 103, 020402 (2009)] which depending on the conditional von Neumann entropy, the Holevo quantity and mutual information. It is shown that the bound obtained in this work is more tighter than other bounds. In addition, using our lower bound, a lower bound for the quantum secret key rate has been obtained. The lower bound is also used to obtain the states for which the strong subadditivity inequality and Koashi-Winter inequality is satisfied with equality.
