Mitigating Source and Detection Noises in Auto-correlative Weak-Value Amplification

Weak-value amplification (WVA) is a post-selection-based technique that amplifies weak physical signals by preparing nearly orthogonal pre- and post-selected quantum states. It is intrinsically limited by various kinds of technical noise, which distorts amplified weak values, especially when discarding photons in post-selection. While prior work established the efficacy of auto-correlative weak-value amplification (AWVA) under Gaussian noise, practical implementations face challenges from band-limited laser-source noise and detection noise. Here, we demonstrate that the AWVA protocol robustly suppresses both laser-power fluctuations and detection noise. Numerical experiments in Simulink further reveal AWVA dual advantage. Under high-power conditions, the noise-reduction superiority of AWVA over WVA becomes increasingly pronounced as input laser power increases. In detection-limited regimes, AWVA achieves an order-of-magnitude lower uncertainty, closely approaching the Cramer-Rao bound. This work demonstrates that AWVA improves precision in both high-power laser-noise-dominated and photon-starved regimes, thereby bridging these operating extremes and advancing precision in applications from gravitational-wave detection to hybrid quantum systems.