Low-ground/High ground capacity regions analysis for Bosonic Gaussian Channels

TL;DR

This paper characterizes the parameter space of Bosonic Gaussian channels, identifying low-ground and high-ground regions based on their information capacities, and provides improved upper bounds for their quantum and private capacities.

Contribution

It introduces a comprehensive framework for analyzing channel concatenations, distinguishing capacity regions, and deriving tighter upper bounds for capacities of Bosonic Gaussian channels.

Findings

Identification of low-ground and high-ground capacity regions

Explicit upper bounds for quantum and private capacities

Improved bounds by combining known results and composition rules

Abstract

We present a comprehensive characterization of the interconnections between single-mode, phaseinsensitive Gaussian Bosonic Channels resulting from channel concatenation. This characterization enables us to identify, in the parameter space of these maps, two distinct regions: low-ground and high-ground. In the low-ground region, the information capacities are smaller than a designated reference value, while in the high-ground region, they are provably greater. As a direct consequence, we systematically outline an explicit set of upper bounds for the quantum and private capacity of these maps, which combine known upper bounds and composition rules, improving upon existing results.