Quantum limits on phase-preserving linear amplifiers

TL;DR

This paper investigates the fundamental quantum limits on phase-preserving linear amplifiers, showing that the added noise distribution is constrained by the ancilla state's Wigner function, extending understanding beyond second moments.

Contribution

It derives the full quantum constraints on the noise distribution of linear amplifiers, linking the added noise to the Wigner function of an ancillary mode, and generalizing the known quantum limit.

Findings

Added noise distribution is determined by the ancilla's Wigner function.

Any phase-preserving amplifier can be modeled as a parametric amplifier with a specific ancilla state.

The quantum limit constrains the entire noise distribution, not just second moments.

Abstract

The purpose of a phase-preserving linear amplifier is to make a small signal larger, regardless of its phase, so that it can be perceived by instruments incapable of resolving the original signal, while sacrificing as little as possible in signal-to-noise. Quantum mechanics limits how well this can be done: a high-gain linear amplifier must degrade the signal-to-noise; the noise added by the amplifier, when referred to the input, must be at least half a quantum at the operating frequency. This well-known quantum limit only constrains the second moments of the added noise. Here we derive the quantum constraints on the entire distribution of added noise: we show that any phase-preserving linear amplifier is equivalent to a parametric amplifier with a physical state for the ancillary mode; the noise added to the amplified field mode is distributed according to the Wigner function of the ancilla state.