Abstract
Quantum systems are always disturbed by environmental noise. We have investigated the influence of the environmental noise on the amplification in weak measurements. Three typical quantum noise processes are discussed in this article. The maximum expectation values of the observables of the measuring device decrease sharply with the strength of the depolarizing and phase damping channels, while the amplification effect of weak measurement is immune to the amplitude damping noise. To obtain significantly amplified signals, we must ensure that the preselection quantum systems are kept away from the depolarizing and phase damping processes.
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