Minimum output entropy of Gaussian channels

TL;DR

This paper proves that the minimum output entropy for all single-mode Gaussian channels is achieved with Gaussian inputs and is additive, enabling the calculation of channel capacities for various Gaussian channels.

Contribution

It establishes the additivity of minimum output entropy for all single-mode Gaussian channels and derives their capacities, a significant advancement in quantum information theory.

Findings

Minimum output entropy is additive for all single-mode Gaussian channels.

Gaussian inputs attain the minimum output entropy.

Channel capacities for several Gaussian channels are explicitly derived.

Abstract

We show that the minimum output entropy for all single-mode Gaussian channels is additive and is attained for Gaussian inputs. This allows the derivation of the channel capacity for a number of Gaussian channels, including that of the channel with linear loss, thermal noise, and linear amplification.