# Phase-preserving linear amplifiers not simulable by the parametric amplifier

## TL;DR

This paper challenges the common belief that all phase-preserving linear amplifiers can be simulated by parametric amplifiers, providing counterexamples and a detailed physical analysis to demonstrate their distinct nature.

## Contribution

The authors construct explicit counterexamples showing that some phase-preserving linear amplifiers cannot be simulated by parametric amplifiers, clarifying the physics behind amplifier-added noise.

## Key findings

- Counterexamples disprove the simulation equivalence.
- Heisenberg-picture analysis explains the physics of the counterexamples.
- Resolves questions about noise in degenerate two-photon amplification.

## Abstract

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.