The amplification of weak measurements under quantum noise

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.