Quantum Noise Limits for Nonlinear, Phase-Invariant Amplifiers
  Any quantum device that amplifies coherent states of a field while preserving their phase generates noise. A nonlinear, phase-invariant amplifier may generate less noise, over a range of input field strengths, than any linear amplifier with the same amplification. We present explicit examples of such nonlinear amplifiers, and derive lower bounds on the noise generated by a nonlinear, phase-invariant quantum amplifier. 
Dmitri Kouznetsov, Roberto Ortega, and Daniel Rohrlich