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IEEE Transactions on Information Theory

Entanglement-Assisted Covert Communication via Qubit Depolarizing Channels

Elyakim Zlotnick, Boulat A. Bash, Uzi Pereg

Published Feb 26, 2025• 8 citations
Publisher

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 innchannel 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 overnuses of a qubit depolarizing channel. The coding scheme employs “weakly” entangled states such that their squared amplitude scales as$O\left ({{{\scriptstyle \text {}^{\scriptstyle 1}}\hspace {-0.224em}/\hspace {-0.112em}{\scriptstyle \sqrt {n}}}}\right)$.

DOI
10.1109/tit.2025.3546191

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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(n)O(\sqrt{n})O(n​) information bits can be reliably and covertly transmitted in nnn channel uses without entanglement assistance. However, Gagatsos et al. (2020) showed that entanglement assistance can increase this scaling to O(nlog⁡(n))O(\sqrt{n}\log(n))O(n​log(n)) for continuous-variable bosonic channels. Here, we present a finite-dimensional parallel, and show that O(nlog⁡(n))O(\sqrt{n}\log(n))O(n​log(n)) covert bits can be transmitted reliably over nnn uses of a qubit depolarizing channel. The coding scheme employs "weakly" entangled states such that their squared amplitude scales as O(1/n)O(1/\sqrt{n})O(1/n​).
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(n)O(\sqrt n )O(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(nlog⁡n)O(\sqrt n \log n)O(n​logn) for continuous-variable bosonic channels. Here, we present a finite-dimensional parallel, and show that O(nlog⁡n)O(\sqrt n \log n)O(n​logn) covert bits can be transmitted reliably over n uses of a qubit depolarizing channel.
We explore covert communication of qubits over an arbitrary quantum channel. Covert communication conceals the transmissions in the channel noise, ensuring that an adversary is unable to detect their presence. We show the achievability of a square root law (SRL) for quantum covert communication similar to that for classical:M(n)nM(n) \sqrt{n}M(n)n​qubits can be transmitted covertly and reliably overnnnuses of a general quantum channel. We lower boundM(n)M (n)M(n)with and without assistance from a two-way covert classical channel. In the former case, we quantify the number of classical covert bits sufficient for our protocol.
We determine the covert capacity for entanglement generation over a noisy quantum channel. While secrecy guarantees that the transmitted information remains inaccessible to an adversary, covert communication ensures that the transmission itself remains undetectable. The entanglement dimension follows a square root law (SRL) in the covert setting, i.e., O(n)O(\sqrt{n})O(n​) Einstein-Podolsky-Rosen (EPR) pairs can be distributed covertly and reliably over nnn channel uses. We begin with covert communication of classical information under a secrecy constraint. We then leverage this result to construct a coding scheme for covert entanglement generation. Single-letter expressions are derived for the covert key-assisted and unassisted secrecy capacities, as well as for the covert entanglement-generation capacity.
We explore covert entanglement generation over the lossy thermal-noise bosonic channel, which is a quantummechanical model of many practical settings, including optical, microwave, and radio-frequency (RF) channels. Covert communication ensures that an adversary is unable to detect the presence of transmissions, which are concealed in channel noise. While covert communication of classical bits is well studied, covert quantum communication and entanglement generation remain largely unexplored. Here, we first show that a square root law (SRL) for covert classical secret communication over the lossy thermal-noise bosonic channel, defining the optimal rate and covert capacityLsec L_{\text{sec }}Lsec ​. The achievable construction relies on position-based coding, sequential decoding, and quadrature phase-shift keying. Furthermore, we adapt the code used in covert secret communication to show that a square root law (SRL) for covert entanglement generation similar to that for classical:LEGnL_{\text{EG}} \sqrt{n}LEG​n​entangled bits (ebits) can be generated covertly and reliably overnnnuses of a bosonic channel. We report a single-letter expression for optimalLEGL_{\text{EG}}LEG​as well as an achievable method. We additionally analyze the performance of covert entanglement generation using single- and dual-rail photonic qubits for varying channel parameters. Despite a performance gap compared to the optimal strategy, these encodings may be more practical for physical implementation.
We explore covert entanglement generation over the lossy thermal-noise bosonic channel, which is a quantum-mechanical model of many practical settings, including optical, microwave, and radio-frequency (RF) channels. Covert communication ensures that an adversary is unable to detect the presence of transmissions, which are concealed in channel noise. We show that a square root law (SRL) for covert entanglement generation similar to that for classical communication: LEGnL_{\rm EG}\sqrt{n}LEG​n​ entangled bits (ebits) can be generated covertly and reliably over nnn uses of a bosonic channel. We report a single-letter expression for optimal LEGL_{\rm EG}LEG​ as well as an achievable method. We additionally analyze the performance of covert entanglement generation using single- and dual-rail photonic qubits, which may be more practical for physical implementation.