Uncertainty regions of observables and state-independent uncertainty relations
Uncertainty regions of observables and state-independent uncertainty relations
复制标题
DOI：
10.1007/s11128-021-03303-w
复制
发表时间：
2021-10
影响因子：
2.5
通讯作者：
Lin Zhang;S. Luo;S. Fei;Junde Wu
中科院分区：
文献类型：
--
作者：
Lin Zhang;S. Luo;S. Fei;Junde Wu
观测量的方差或偏差之和的最优状态无关下界对于越来越多的达到不确定度限制的实验具有重要意义。我们提出了一个计算方差或偏差的紧测不准关系的框架，通过确定不确定区域，这些不确定区域由两个或两个以上的量子观测量在随机量子态中的元组形成，这些元组由均匀Haar测度在纯化态上诱导而成。从这些不确定区域的解析公式出发，我们给出了两个、三个和任意多个观测量的方差或偏差之和所满足的与状态无关的不确定不等式，并由此导出了二体和三体系统的友态纠缠的实验检测准则.
The optimal state-independent lower bounds for the sum of variances or deviations of observables are of significance for the growing number of experiments that reach the uncertainty limited regime. We present a framework for computing the tight uncertainty relations of variance or deviation via determining the uncertainty regions, which are formed by the tuples of two or more of quantum observables in random quantum states induced from the uniform Haar measure on the purified states. From the analytical formulae of these uncertainty regions, we present state-independent uncertainty inequalities satisfied by the sum of variances or deviations of two, three and arbitrary many observables, from which experimentally friend entanglement detection criteria are derived for bipartite and tripartite systems.