  Weak value amplification (WVA) is a metrological protocol that amplifies
ultra-small physical effects. However, the amplified outcomes necessarily occur
with highly suppressed probabilities, leading to the extensive debate on
whether the overall measurement precision is improved in comparison to that of
conventional measurement (CM). Here, we experimentally demonstrate the
unambiguous advantages of WVA that overcome practical limitations including
noise and saturation of photo-detection and maintain a shot-noise-scaling
precision for a large range of input light intensity well beyond the dynamic
range of the photodetector. The precision achieved by WVA is six times higher
than that of CM in our setup. Our results clear the way for the widespread use
of WVA in applications involving the measurement of small signals including
precision metrology and commercial sensors.
