Coherent information of one-mode Gaussian channels -- the general case of nonzero added classical noise

TL;DR

This paper proves that for certain one-mode Gaussian channels with nonzero classical noise, the maximum coherent information is achieved at infinite input power, filling a gap in the understanding of these channels.

Contribution

It extends the understanding of coherent information maximization to channels with nonzero classical noise, specifically for lossy, amplifying, and additive noise classes.

Findings

Maximum coherent information achieved at infinite input power for nonzero noise channels

Analysis covers lossy, amplifying, and additive classical noise channels

Coherent information vanishes for other channel classes

Abstract

We prove that whenever the coherent information of a one-mode Gaussian channel is non-zero its supremum is achieved for the infinite input power. This is a well established fact for the zero added classical noise, whereas the nonzero case has not been studied in detail. The presented analysis fills the gap for three canonical classes of one-mode Gaussian channels: the lossy, amplifying and additive classical noise channel class. For the remaining one-mode Gaussian channel classes the coherent information is known to vanish.