  The influence of outside quantum noises on the amplification of weak
measurements is investigated. Three typical quantum noises are discussed. The
maximum values of the pointer's shifts decrease sharply with the strength of
the depolarizing channel and phase damping. In order to obtain significant
amplified signals, the preselection quantum systems must be kept away from the
two quantum noises. Interestingly, the amplification effect is immune to the
amplitude damping noise.
