Mitigating source and detection noises in autocorrelative weak-value amplification

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