Gaussian capacity of the quantum bosonic channel with additive correlated Gaussian noise

TL;DR

This paper introduces an algorithm to calculate the Gaussian classical capacity of quantum bosonic memory channels with correlated Gaussian noise, applicable across all input energies and demonstrating near-optimal performance of simple encoding schemes.

Contribution

The paper develops a comprehensive algorithm for capacity calculation of Gaussian bosonic channels with correlated noise, extending previous methods to all energy levels and illustrating with a Gauss-Markov noise example.

Findings

The algorithm applies to channels with certain noise correlations.

Optimal entangled inputs significantly enhance transmission rates.

Simple coherent-state encoding achieves at least 90% of the channel capacity.

Abstract

We present an algorithm for calculation of the Gaussian classical capacity of a quantum bosonic memory channel with additive Gaussian noise. The algorithm, restricted to Gaussian input states, is applicable to all channels with noise correlations obeying certain conditions and works in the full input energy domain, beyond previous treatments of this problem. As an illustration, we study the optimal input states and capacity of a quantum memory channel with Gauss-Markov noise [J. Sch\"afer, Phys. Rev. A 80, 062313 (2009)]. We evaluate the enhancement of the transmission rate when using these optimal entangled input states by comparison with a product coherent-state encoding and find out that such a simple coherent-state encoding achieves not less than 90% of the capacity.