Estimating Quantum and Private capacities of Gaussian channels via degradable extensions

TL;DR

This paper develops upper bounds on the quantum and private capacities of Gaussian channels using degradable extensions, providing state-of-the-art results in specific parameter regimes such as low temperature and high transmissivity.

Contribution

It introduces a novel method of using degradable extensions to estimate capacities of Gaussian channels, advancing the understanding of their limits.

Findings

Upper bounds are established for thermal attenuators at low temperature and high transmissivity.

Bounds are improved for additive Gaussian noise channels at low temperature.

Results include high-temperature and intermediate amplification regimes for thermal amplifiers.

Abstract

We present upper bounds on the quantum and private capacity of single-mode, phase-insentitive Bosonic Gaussian Channels based on degradable extensions. Our findings are state-of-the-art in the following parameter regions: low temperature and high transmissivity for the thermal attenuator, low temperature for additive Gaussian noise, high temperature and intermediate amplification for the thermal amplifier.