江汉大学学报（自然科学版）

柯西不等式在酉不确定性的研究中有着重要应用,利用柯西不等式改进其本身并将其应用于酉不确定性的计算中。首先,运用以低维柯西不等式来优化高维柯西不等式的思想构造了第一个柯西不等式序列;然后,通过引入凸函数,得到了第二个柯西不等式序列;最后,将构造的柯西不等式序列应用于基于方差乘积的两个酉算子的不确定性实例研究中。结果表明,所构造的柯西不等式序列能有效地改进两个酉算子基于方差乘积的不确定性的界。

Cauchy's inequality has an important application in the study of unitary uncertainty. The authors use Cauchy's inequality to improve itself and apply it to the calculation of unitary uncertainty. Firstly,the idea of using low-dimensional Cauchy's inequality to optimize high-dimensional Cauchy's inequality is used to obtain the first sequence of Cauchy's inequality. Then, by introducing a convex function, the second sequence of Cauchy's inequality is obtained. Finally,the obtained sequence of Cauchy's inequality is applied to study the variance-based quantum uncertainty. The results show that the Cauchy's inequality sequence constructed by us can effectively optimize the bounds of variance product-based uncertainty for two unitary operators.