  It is known that weak measurement can significantly amplify the mean of
measurement results, sometimes out of the range limited in usual quantum
measurement. This fact, as actively demonstrated recently in both theory and
experiment, implies the possibility to estimate a very small parameter using
the weak measurement technique. But does the weak measurement really bring
about the increase of "information" for parameter estimation? This paper
clarifies that, in a general situation, the answer is NO; more precisely, the
weak measurement cannot further decrease the lower bound of the estimation
error, i.e. the so-called Cram\'{e}r-Rao bound, which is proportional to the
inverse of the quantum Fisher information.

Quantum Physics