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