The conditional entropy power inequality for Gaussian quantum states

TL;DR

This paper extends the quantum entropy power inequality to include conditional entropies for Gaussian states, providing a proof and discussing implications for quantum communication channels.

Contribution

It introduces a generalized conditional entropy power inequality for Gaussian quantum states, with a proof based on symplectic spectrum perturbation theory.

Findings

Established a conditional entropy power inequality for Gaussian states

Provided a proof using symplectic spectrum perturbation theory

Discussed implications for entanglement-assisted classical communication

Abstract

We propose a generalization of the quantum entropy power inequality involving conditional entropies. For the special case of Gaussian states, we give a proof based on perturbation theory for symplectic spectra. We discuss some implications for entanglement-assisted classical communication over additive bosonic noise channels.