摘要翻译：
设$A_1,...,A_n$为复自伴矩阵，设$\Rho$为密度矩阵。Robertson测不准原理$$det(cov_\rho(A_h,A_j))\geq det(-\frac{i}{2}Tr(\rho[A_h,A_j]))$$根据交换子$[A_h,A_j]$给出了量子广义协方差的一个界。右矩阵是反对称的，因此，在奇数情况下，$n=2m+1$的界是平凡的（等于零）。设$f$为任意归一化对称算子单调函数，设$<\cdot>_{\rho,f}$为关联的量子Fisher信息。本文证明了不等式$$det(cov_\rho(A_h,A_j))\geq det(\frac{f(0)}{2}<i[\rho,A_h],i[\rho,A_j]>_{\rho,f})$$,该不等式利用交换子$[\rho,A_h]$给出了{\mathbb N}$中任意$N\的非平凡界。
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英文标题：
《A Robertson-type Uncertainty Principle and Quantum Fisher Information》
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作者：
Paolo Gibilisco, Daniele Imparato, Tommaso Isola
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Mathematical Physics        数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics        数学
二级分类：Mathematical Physics        数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  Let $A_1,...,A_N$ be complex selfadjoint matrices and let $\rho$ be a density matrix. The Robertson uncertainty principle $$ det (Cov_\rho(A_h,A_j)) \geq det (- \frac{i}{2} Tr (\rho [A_h,A_j])) $$ gives a bound for the quantum generalized covariance in terms of the commutators $ [A_h,A_j]$. The right side matrix is antisymmetric and therefore the bound is trivial (equal to zero) in the odd case $N=2m+1$.   Let $f$ be an arbitrary normalized symmetric operator monotone function and let $<\cdot, \cdot >_{\rho,f}$ be the associated quantum Fisher information. In this paper we prove the inequality $$ det (Cov_\rho (A_h,A_j)) \geq det (\frac{f(0)}{2} < i[\rho, A_h],i[\rho,A_j] >_{\rho,f}) $$ that gives a non-trivial bound for any $N \in {\mathbb N}$ using the commutators $[\rho,A_h]$.
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PDF链接：
https://arxiv.org/pdf/707.1231