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The weak-value-amplification (WVA) technique has been extensively consideredand debated in the field of quantum precision measurement, largely owing to thereduced Fisher information caused by the low probability of successfulpost-selection. %% In this work we show that, rather than the Gaussian meterstate as typically considered, using the optical coherent state as a meter, theWVA measurement can definitely outperform the conventional measurement notinvolving the strategy of post-selection. %% We also show that thepost-selection procedure involved in the WVA scheme can make a mixture ofcoherent states work better than a pure coherent state with identical averagephoton numbers. This is in sharp contrast to the claim proved in the absence ofpost-selection. The post-selection strategy can also result in the precision ofHeisenberg (or even "super-Heisenberg") scaling with the photon numbers, butwithout using any expensive quantum resources. %% The present work maystimulate further investigations for the potential of the post-selectionstrategy in quantum precision measurements.

Fisher information analysis on post-selection involved quantum precision measurements using optical coherent states