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It is commonly accepted that a parametric amplifier can simulate aphase-preserving linear amplifier regardless of how the latter is realized[Caves et al., Phys. Rev. A 86, 063802 (2012)]. If true, this reduces allphase-preserving linear amplifiers to a single familiar model. Here we disprovethis claim by constructing two counterexamples. A detailed discussion of thephysics of our counterexamples is provided. It is shown that aHeisenberg-picture analysis facilitates a microscopic explanation of thephysics. This also resolves a question about the nature of amplifier-addednoise in degenerate two-photon amplification.

Phase-preserving linear amplifiers not simulable by the parametric amplifier