Evaluating capacities of Bosonic Gaussian channels

TL;DR

This paper develops methods to compute and estimate key capacity-related quantities for Bosonic Gaussian channels, providing explicit bounds and evaluations for practical one-mode channels with noise and amplification.

Contribution

It introduces a new quantity involving the transpose operation that bounds quantum capacity and provides explicit evaluations for common channel models.

Findings

Derived bounds for quantum and classical capacities.

Introduced a new upper bound involving transpose operation.

Explicitly evaluated capacities for one-mode channels with noise.

Abstract

We show how to compute or at least to estimate various capacity-related quantities for Bosonic Gaussian channels. Among these are the coherent information, the entanglement assisted classical capacity, the one-shot classical capacity, and a new quantity involving the transpose operation, shown to be a general upper bound on the quantum capacity, even allowing for finite errors. All bounds are explicitly evaluated for the case of a one-mode channel with attenuation/amplification and classical noise.