最近，Chau [Quant.通知。11，721（2011）]发现了关于$n$维酉算子的度量和伪度量族，其可以被解释为将一个酉算子变换为另一个酉算子所需的最小资源（由某些紧密的量子速度限制边界给出）。这个结果与${\mathbb R}^n$上的加权$\ell^1$ -范数密切相关.在这里，我们推广了这一发现，通过显示每个加权$\ell^p$ -范数${\mathbb R}^n$与$1\le p \le \limitingp$诱导一个度量和伪度量的$n$维酉算子与量子信息理论的意义，涉及到某些严格的量子速度极限的界限。此外，我们还研究了这类度量和伪度量的存在性与量子速度极限之间的对应关系。
英文摘要：
Recently, Chau [Quant. Inform. & Comp. 11, 721 (2011)] found a family of metrics and pseudo-metrics on $n$-dimensional unitary operators that can be interpreted as the minimum resources (given by certain tight quantum speed limit bounds) needed to transform one unitary operator to another. This result is closely related to the weighted $\ell^1$-norm on ${\mathbb R}^n$. Here we generalize this finding by showing that every weighted $\ell^p$-norm on ${\mathbb R}^n$ with $1\le p \le \limitingp$ induces a metric and a pseudo-metric on $n$-dimensional unitary operators with quantum information-theoretic meanings related to certain tight quantum speed limit bounds. Besides, we investigate how far the correspondence between the existence of metrics and pseudo-metrics of this type and the quantum speed limits can go.
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）
Quantum equilibration and measurements -- bounds on speeds, Lyapunov exponents, and transport coefficients obtained from the uncertainty relations and their comparison with experimental data
