Progress and perspectives on weak-value amplification

Weak-value amplification (WVA) is a metrological protocol that effectively amplifies ultra-small physical effects, making it highly applicable in the fields of quantum sensing and metrology. However, the amplification effect is achieved through post-selection, which leads to a significant decrease in signal intensity. Consequently, there is a heated debate regarding the trade-off between the amplification effect and the success probability of post-selection, questioning whether WVA surpasses conventional measurement (CM) in terms of measurement precision. Extensive research indicates that the specific theoretical assumptions and experimental conditions play crucial roles in determining the respective advantages of WVA and CM. WVA provides new perspectives for recognizing the important role of post-selection in precision metrology. It demonstrates significant advantages in two aspects: (i) WVA based on the phase space interaction provides feasible strategies to practically achieve the Heisenberg-scaling precision using only classical resources. (ii) WVA exhibits robustness against certain types of technical noise and imperfections of detectors. Moreover, WVA allows for various modifications to extend the applicable scope and enhance the metrological performance in corresponding situations. Despite substantial progress in recent years, the inherent connection between the advantages of WVA and its unique features remains incompletely understood. In this paper, we systematically review the recent advances in the WVA scheme, with a particular focus on the ultimate precision of WVA under diverse conditions. Our objective is to provide a comprehensive perspective on the benefits of WVA in precision measurement and facilitate the realization of its full potential.