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.

中文翻译：

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弱值放大的进展与展望


弱值放大（WVA）是一种有效放大超微小物理效应的计量协议，使其在量子传感和计量领域具有很高的适用性。然而，放大效果是通过后选择实现的，这导致信号强度显着下降。因此，关于放大效应和后选择成功概率之间的权衡存在着激烈的争论，质疑WVA在测量精度方面是否超越了传统测量（CM）。大量研究表明，具体的理论假设和实验条件对于确定WVA和CM各自的优势起着至关重要的作用。 WVA 为认识后选择在精密计量中的重要作用提供了新的视角。它在两个方面表现出显着的优势：（i）基于相空间相互作用的WVA提供了可行的策略，仅使用经典资源即可实际实现海森堡标度精度。 (ii) WVA 对某些类型的技术噪声和探测器缺陷表现出鲁棒性。此外，WVA允许进行各种修改，以扩展适用范围并增强相应情况下的计量性能。尽管近年来取得了实质性进展，但 WVA 的优势及其独特功能之间的内在联系仍然不完全清楚。在本文中，我们系统地回顾了 WVA 方案的最新进展，特别关注不同条件下 WVA 的最终精度。我们的目标是提供关于 WVA 在精密测量方面的优势的全面视角，并促进其全部潜力的实现。