  The weak-value-amplification (WVA) technique has been extensively considered
and debated in the field of quantum precision measurement, largely owing to the
reduced Fisher information caused by the low probability of successful
post-selection. %% In this work we show that, rather than the Gaussian meter
state as typically considered, using the optical coherent state as a meter, the
WVA measurement can definitely outperform the conventional measurement not
involving the strategy of post-selection. %% We also show that the
post-selection procedure involved in the WVA scheme can make a mixture of
coherent states work better than a pure coherent state with identical average
photon numbers. This is in sharp contrast to the claim proved in the absence of
post-selection. The post-selection strategy can also result in the precision of
Heisenberg (or even "super-Heisenberg") scaling with the photon numbers, but
without using any expensive quantum resources. %% The present work may
stimulate further investigations for the potential of the post-selection
strategy in quantum precision measurements.
