Compound Channel Capacities under Energy Constraints and Application

TL;DR

This paper establishes a coding theorem for compound channel models in quantum communication, providing explicit capacity formulas and insights for receiver design under various uncertainties.

Contribution

It introduces a comprehensive coding theorem for practical quantum compound channels and derives explicit capacity formulas for Gaussian cases with unknown parameters.

Findings

Explicit capacity formulas for Gaussian quantum compound channels.

Analytical insights into optimal receiver parameter choices.

Demonstration of compound channel models guiding receiver design.

Abstract

Compound channel models offer a simple and straightforward way of analyzing the stability of decoder design under model variations. With this work we provide a coding theorem for a large class of practically relevant compound channel models. We give explicit formulas for the cases of the Gaussian classical-quantum compound channels with unknown noise, unknown phase and unknown attenuation. We show analytically how the classical compound channel capacity formula motivates nontrivial choices of the displacement parameter of the Kennedy receiver. Our work demonstrates the value of the compound channel model as a method for the design of receivers in quantum communication.