Methods for Estimating Capacities and Rates of Gaussian Quantum Channels

TL;DR

This paper develops optimization methods to estimate the capacities of Gaussian quantum channels, analyzing single and multi-mode cases, and compares different environmental conditions to understand their impact on capacity and transmission rates.

Contribution

It introduces a comprehensive framework for estimating Gaussian channel capacities, including methods for both single and multi-mode channels, and evaluates the effects of environment states and memory.

Findings

Capacity depends on channel parameters and environment states.

Memory effects and inter-mode correlations influence capacity.

Transmission rates can be approximated using the developed methods.

Abstract

Optimization methods aimed at estimating the capacities of a general Gaussian channel are developed. Specifically evaluation of classical capacity as maximum of the Holevo information is pursued over all possible Gaussian encodings for the lossy bosonic channel, but extension to other capacities and other Gaussian channels seems feasible. Solutions for both memoryless and memory channels are presented. It is first dealt with single use (single-mode) channel where the capacity dependence from channel's parameters is analyzed providing a full classification of the possible cases. Then it is dealt with multiple uses (multi-mode) channel where the capacity dependence from the (multi-mode) environment state is analyzed when both total environment energy and environment purity are fixed. This allows a fair comparison among different environments, thus understanding the role of memory (inter-mode correlations) and phenomenon like superadditivity of the capacity. The developed methods are also used for deriving transmission rates with heterodyne and homodyne measurements at the channel output. Classical capacity and transmission rates are presented within a unique framework where the rates can be treated as logarithmic approximations of the capacity.