Entanglement-Assisted Covert Communication via Qubit Depolarizing Channels

TL;DR

The paper addresses whether pre-shared entanglement can boost covert communication over a finite-dimensional qubit depolarizing channel. It introduces a scheme using weakly entangled states with $\alpha_n=O(1/\sqrt{n})$ and position-based coding to achieve a covert rate scaling of $O(\sqrt{n}\log n)$ in the nontrivial Willie-observation regime, while analyzing two other scenarios where covert communication is impossible or trivial. The main result is a rigorous lower bound on the entanglement-assisted covert capacity and a demonstration that entanglement can materially increase the information-carrying capability under covertness constraints, with an energy-constraint interpretation linking the gain to $\log(1/E)$ under $E_n\sim 1/\sqrt{n}$. This work extends the SRL-violating benefit of entanglement from continuous-variable bosonic channels to a finite-dimensional setting, offering new insights for covert quantum communications and guiding future work on general channels and resource-efficient implementations.

Abstract

We consider entanglement-assisted communication over the qubit depolarizing channel under the security requirement of covert communication, where not only the information is kept secret, but 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 $O(1/\sqrt{n})$.

Figures (2)

• Figure 1: Entanglement-assisted coding for covert communication over a quantum channel $\mathcal{N}_{A\rightarrow B W}$. Alice and Bob access entangled resources in systems $T_{A}$ and $T_{B}$, respectively. Message $m$ is encoded by applying the map $\mathcal{F}^{(m)}_{ T_A \rightarrow A^n}$ to the entangled system $T_A$. Alice decides whether to transmit to Bob (Case 1) or not (Case 0). A switch connects the channel to the encoder in Case 1 or to a zero sequence $\ket{0}^{\otimes n}$ in Case 0. Alice transmits the systems $A^n$ over the quantum channel. Bob receives the channel output systems $B^n$, and performs a joint decoding measurement on the systems $B^n$ and $T_B$, using a POVM $\mathcal{D}_{B^n T_B}$. Willie receives the output systems $W^n$, and performs a binary measurement to test whether transmission has taken place.
• Figure 2: The lower bound on the entanglement-assisted covert capacity of Scenario 3 in Theorem \ref{['Theorem:main_theorem']}, as a function of the noise parameter $q$.

Theorems & Definitions (24)

• Remark 1
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• Remark 3
• Remark 4
• Definition 1
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• Definition 2
• Remark 7
• Definition 3