# Quantum amplification and purification of noisy coherent states

## TL;DR

This paper explores the optimal quantum processes that interpolate between amplification and purification of noisy coherent states, demonstrating Gaussian optimality and probabilistic advantages, with feasible experimental implementations.

## Contribution

It identifies the optimal Gaussian processes for quantum amplification and purification, highlighting non-Gaussian probabilistic benefits and providing benchmarks for experimental validation.

## Key findings

- Optimal deterministic processes are Gaussian.
- Non-Gaussian processes offer probabilistic advantages.
- Benchmarks enable experimental certification.

## Abstract

Quantum-limited amplifiers increase the amplitude of quantum signals at the price of introducing additional noise. Quantum purification protocols operate in the reverse way, by reducing the noise while attenuating the signal. Here we investigate a scenario that interpolates between these two extremes. We search for the optimal physical process that generates $M$ approximate copies of pure and amplified coherent state, starting from $N$ copies of a noisy coherent state with Gaussian modulation. We prove that the optimal deterministic processes are always Gaussian, whereas non-Gaussianity powers up probabilistic advantages in suitable parameter regimes. The optimal processes are experimentally feasible, both in the deterministic and in the probabilistic scenario. In view of this fact, we provide benchmarks that can be used to certify the experimental demonstration of the quantum-enhanced amplification and purification of coherent states.