  Weak value amplification (WVA) is a technique in which one can magnify the
apparent strength of a measurement signal. Some have claimed that WVA can
outperform more conventional measurement schemes in parameter estimation.
Nonetheless, a significant body of theoretical work has challenged this
perspective, suggesting WVA to be fundamentally sub-optimal. Optimal
measurements may not be practical, however. Two practical considerations that
have been conjectured to afford a benefit to WVA over conventional measurement
are certain types of noise and detector saturation. Here, we report a
theoretical study of the role of saturation and pixel noise in WVA-based
measurement, in which we carry out a Bayesian analysis of the Fisher
information available using a saturable, pixelated, digitized, and/or noisy
detector. We draw two conclusions: first, that saturation alone does not confer
an advantage to the WVA approach over conventional measurement, and second,
that WVA can outperform conventional measurement when saturation is combined
with intrinsic pixel noise and/or digitization.
