Quantum noise limits for a class of nonlinear amplifiers*

We introduce a class of nonlinear amplifier input-output relations that allow the measurement of any normal operator using linear measurements with only vacuum fluctuations added at the output. In the limit of large gain, such devices would effectively implement perfect measurements of nonlinear operators in the same way that linear amplifiers permit effectively perfect linear measurements even when paired with realistic, noisy measurement devices. We analyze the application of these amplifiers to photon number measurements and state estimation.