Nonlinear amplifiers: quantum limits and generalized longitudinal readout

Nonlinear amplifiers such as the transistor are ubiquitous in classical technology, but their quantum analogues are not well understood. We introduce a class of nonlinear amplifiers that amplify any normal operator and add only a half-quantum of vacuum noise at the output. In the large-gain limit, when used in conjunction with a noisy linear detector, these amplifiers implement ideal measurements of the normal operator. It turns out a special case of these amplifiers is the longitudinal interaction. Thus longitudinal readout can be understood through the lens of nonlinear amplification.