量子系统上的弱值测量: 理论、实现、应用及开放性问题
Weak-value measurements at quantum systems: theory, realizations, applications and open problems

量子弱值测量在1988年被首次提出, 目前已成为具备微弱信号放大、获得复数值观测结果和观测量子系统 非经典特征等功能的实验工具, 并且它与投影测量存在明显区别. 关于弱值的物理解释, 人们目前尚未达成完全一 致的观点, 而本文采用实用的观点, 根据其数学关系式, 认为弱值是一个与测量操作过程紧密相关的条件观测期望 值. 本综述首先对弱值测量一般过程展开理论描述, 并对该过程中关键步骤的目的加以说明. 其次, 集中展示文献 报道的4个不同物理实现方式的弱值测量实验方案. 再次, 介绍弱值测量的3种典型实验应用, 以及每种应用的具体 要求. 最后, 探讨弱值测量今后的研究方向, 重点关注以下4个开放性问题: 改进物理实现方式、突破应用条件限制、 分析实验误差影响、探索其他应用可能.
First proposed in 1988, the quantum weak-value measurement has become an experimental tool with functions of amplifying small signals, obtaining complex-number-valued observable results and measuring nonclassical features in quantum systems, and it is distinctly different from the projective measurement. Nowadays researchers have not reached a consensus on the physical interpretation of a weak-value. According to the mathematical expression, the weak-value is regarded from a practical view as a conditioned observable expectation related to the measurement operational procedure in this review. First, the theoretical description is presented for the general procedure of the weak-value measurement, and the purpose of the key step in the procedure is explained. Second, four experiment schemes with different physical realizations published in multiple research papers are assembled here. Third, this review presents three typical applications of the weakvalue measurement and their corresponding requirements. Last, future research directions on the weak-value measurement are discussed through focusing on these four open problems: improving physical realization manners, overpassing the applicative condition limitation, analyzing experimental error influence and exploring other application possibilities.