论文标题
标准对称性方差与连贯性，不确定性和纠缠的应用
Standard symmetrized variance with applications to coherence, uncertainty and entanglement
论文作者
论文摘要
方差是量子信息理论中普遍存在的数量。在给定基础上，我们考虑在纯状态的所有可能排列下可观察到的固定对角线的平均方差，并将其称为对称方差。此外，我们研究了对称方差的分析表达，并发现这种表达在分解形式中，其中两个因素分别取决于对角线可观察到的量子状态。通过移动与可观察到的对角线相对应的因子，我们引入了称为纯状态的标准对称方差的概念，该概念与对角线无关可观察到。然后，我们以三种不同的方式将标准对称方差扩展到混合状态，这分别表征了不确定性，辅助的连贯性和连贯性。这些数量进行了分析评估，并建立了它们之间的关系。此外，我们表明标准对称方差也是两部分系统的纠缠措施。这样，量子状态的这些不同量子性被方差统一。
Variance is a ubiquitous quantity in quantum information theory. Given a basis, we consider the averaged variances of a fixed diagonal observable in a pure state under all possible permutations on the components of the pure state and call it the symmetrized variance. Moreover we work out the analytical expression of the symmetrized variance and find that such expression is in the factorized form where two factors separately depends on the diagonal observable and quantum state. By shifting the factor corresponding to the diagonal observable, we introduce the notion named the standard symmetrized variance for the pure state which is independent of the diagonal observable. We then extend the standard symmetrized variance to mixed states in three different ways, which characterize the uncertainty, the coherence and the coherence of assistance, respectively. These quantities are evaluated analytically and the relations among them are established. In addition, we show that the standard symmetrized variance is also an entanglement measure for bipartite systems. In this way, these different quantumness of quantum states are unified by the variance.
