Entanglement-Assisted Covert Communication via Qubit Depolarizing Channels

Abstract

We consider entanglement-assisted communication over the qubit depolarizing channel under the security requirement of covert communication, where the transmission itself must be concealed from detection by an adversary. Previous work showed that $O(\sqrt {n})$ information bits can be reliably and covertly transmitted in n channel uses without entanglement assistance. However, Gagatsos et al. (2020) showed that entanglement assistance can increase this scaling to $O(\sqrt {n}\log {n})$ for continuous-variable bosonic channels. Here, we present a finite-dimensional parallel, and show that $O(\sqrt {n}\log {n})$ covert bits can be transmitted reliably over n uses of a qubit depolarizing channel. The coding scheme employs “weakly” entangled states such that their squared amplitude scales as $O\left ({{{\scriptstyle \text {}^{\scriptstyle 1}}\hspace {-0.224em}/\hspace {-0.112em}{\scriptstyle \sqrt {n}}}}\right)$ .