Title: Evaluating the quantum optimal biased bound in a unitary evolution process Show Chinese title

Title: 评估单位演化过程中的量子最优偏差界限

Abstract: Seeking the available precision limit of unknown parameters is a significant task in quantum parameter estimation. One often resorts to the widely utilized quantum Cramer-Rao bound (QCRB) based on unbiased estimators to finish this task. Nevertheless, most actual estimators are usually biased in the limited number of trials. For this reason, we introduce two effective error bounds for biased estimators based on a unitary evolution process in the framework of the quantum optimal biased bound. Furthermore, we show their estimation performance by two specific examples of the unitary evolution process, including the phase encoding and the SU(2) interferometer process. Our findings will provide an useful guidance for finding the precision limit of unknown parameters. Show Chinese abstract

Abstract: 寻找未知参数的可用精度极限是量子参数估计中的一个重要任务。 人们通常借助基于无偏估计量的广泛使用的量子Cramer-Rao界（QCRB）来完成此任务。 然而，大多数实际估计量在有限的试验次数下通常是偏差的。 为此，我们在量子最优偏差界限框架下，基于一个单位演化过程，引入了两种针对偏差估计量的有效误差界限。 此外，我们通过两个具体的单位演化过程示例展示了它们的估计性能，包括相位编码和SU(2)干涉仪过程。 我们的研究结果将为寻找未知参数的精度极限提供有用的指导。