论文标题
有限量子系统的GINI指数的不确定性关系
Uncertainty relations in terms of the Gini index for finite quantum systems
论文作者
论文摘要
洛伦兹的值和Gini指数是数学经济学中流行的数量，在这里在具有有限维的希尔伯特空间的量子系统中使用。他们量化了与正顺序基础相关的概率分布中的不确定性。结果表明，洛伦兹值是超脱脂函数，而吉尼指数是亚addive函数。在位置和动量状态下，两个Gini指数总和的所有密度矩阵上的上述矩阵用于定义一个不确定性系数，该系数量化了量子系统中不确定性的不确定性。结果表明，不确定性系数为正，并且给出了上限。各种例子证明了这些想法。
Lorenz values and the Gini index are popular quantities in Mathematical Economics, and are used here in the context of quantum systems with finite-dimensional Hilbert space. They quantify the uncertainty in the probability distribution related to an orthonormal basis. It is shown that Lorenz values are superadditive functions and the Gini indices are subadditive functions. The supremum over all density matrices of the sum of the two Gini indices with respect to position and momentum states, is used to define an uncertainty coefficient which quantifies the uncertainty in the quantum system. It is shown that the uncertainty coefficient is positive, and an upper bound for it is given. Various examples demonstrate these ideas.
