# Upper bounds on the quantum capacity for general attenuator and amplifier

## TL;DR

This paper derives new upper bounds on the quantum capacity of general attenuator and amplifier channels with diverse noise types, using quantum entropy inequalities, and provides tight bounds in specific regimes.

## Contribution

It introduces generalized upper bounds for quantum capacity of noisy attenuator and amplifier channels, extending beyond Gaussian noise, using quantum entropy power inequalities.

## Key findings

- Tighter upper bounds near transmissivity of one
- Lower bounds established via Gaussian optimizer
- Bounds are narrow at low input energy

## Abstract

There have been several upper bounds on the quantum capacity of the single-mode Gaussian channels with thermal noise, such as thermal attenuator and amplifier. We consider a class of attenuator and amplifier with more general noises, including squeezing or even non-Gaussian one. We derive new upper bounds on the energy-constrained quantum capacity of those channels by using the quantum conditional entropy power inequality. Also, we obtain lower bounds for the same channels by means of Gaussian optimizer with fixed input entropy. They give narrow bounds when the transmissivity is near unity and the energy of input state is low.