In this paper, we first provide three general norm inequalities, which are used to give new uncertainty relations of any finite observables and quantum channels via metric-adjusted skew information. The results are applicable to its special cases as Wigner-Yanase-Dyson skew information. In quantifying the uncertainty of channels, we discuss two types of lower bounds and compare the tightness between them, meanwhile, a tight lower bound is given. The uncertainty relations obtained by us are stronger than the existing ones. To illustrate our results, we give several specific examples.
A note on uncertainty relations of metric-adjusted skew information
不确定原理是量子力学的基本特征之一，在量子信息处理中起着至关重要的作用。研究了基于度量调整偏斜信息的有限量子观测量的不确定关系。受论文[Physical Review A 104，052414（2021）]的启发，我们根据不同的范数不等式建立了更紧密的不确定性关系。自然地，我们将该方法推广到量子信道和幺正算符的度量调整偏斜信息的不确定关系。由于Wigner-Yanase-Dyson斜信息和量子费舍尔信息都是对应于不同Morozova-Chentsov函数的度量调整的斜信息的特殊情况，我们的结果推广了一些现有的不确定关系.最后给出了具体的算例来说明本文方法的优越性。
Quantum average correlations and complementarity relations via metric-adjusted skew information
College of Science, National University of Defense Technology（国防科技大学理学院）；School of Mathematics and Statistics, Changsha University of Science and Technology（长沙理工大学数学与统计学院）；Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology（长沙理工大学湖南省工程数学建模与分析重点实验室）；School of Mathematical Sciences, Capital Normal University（首都师范大学数学科学学院）
