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IEEE International Symposium on Information Theory (ISIT)

Resource-Efficient Entanglement-Assisted Covert Communications over Bosonic Channels

Shiyuan Wang, Shang-Jen Su, Matthieu R. Bloch

Published Jul 7, 2024• 9 citations
Publisher

Abstract

We revisit the problem of entanglement-assisted covert communication over bosonic channels and show that the$\text{benefits}$of entanglement can be achieved with fewer entanglement resources than previously identified. Specifically, we show that$\mathcal{O}(\sqrt{n}\log n)$covert and reliable bits can be exchanged using$\omega(\sqrt{n})\cap o(n)$Two-Mode Squeezed-Vacuum (TMSV) pairs and$\omega(1)\cap o(\sqrt{n})$secret-key bits. The conceptual approach behind the result is to combine 1) soft-covering and secret-key resources as a coordination mechanism and 2) superposition coding in the form of a two-layer On-Off Keying (OOK) and Phase Shift Keying (PSK) to index channel uses in which TMSV pairs are encoded. This approach is related to the idea of quantum trade-off coding, specialized and extended to the covert communication setting. Our technical contribution is to develop one-shot bounds then specialized to bosonic channels.

DOI
10.1109/isit57864.2024.10619663

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We revisit the problem of entanglement-assisted covert communication over bosonic channels and show that thebenefits\text{benefits}benefitsof entanglement can be achieved with fewer entanglement resources than previously identified. Specifically, we show thatO(nlog⁡n)\mathcal{O}(\sqrt{n}\log n)O(n​logn)covert and reliable bits can be exchanged usingω(n)∩o(n)\omega(\sqrt{n})\cap o(n)ω(n​)∩o(n)Two-Mode Squeezed-Vacuum (TMSV) pairs andω(1)∩o(n)\omega(1)\cap o(\sqrt{n})ω(1)∩o(n​)secret-key bits. The conceptual approach behind the result is to combine 1) soft-covering and secret-key resources as a coordination mechanism and 2) superposition coding in the form of a two-layer On-Off Keying (OOK) and Phase Shift Keying (PSK) to index channel uses in which TMSV pairs are encoded. This approach is related to the idea of quantum trade-off coding, specialized and extended to the covert communication setting. Our technical contribution is to develop one-shot bounds then specialized to bosonic channels.
We consider the problem of covert communication over the entanglement-assisted (EA) bosonic multiple access channel (MAC). We derive a closed-form achievable rate region for the general EA bosonic MAC using high-order phase-shift keying (PSK) modulation. Specifically, we demonstrate that in the low-photon regime the capacity region collapses into a rectangle, asymptotically matching the point-to-point capacity as multi-user interference vanishes. We also characterize an achievable covert throughput region, showing that entanglement assistance enables an aggregate throughput scaling of O(nlog⁡n)O(\sqrt{n} \log n)O(n​logn) covert bits with the block length nnn for both senders, surpassing the square-root law as in the point-to-point case. Our analysis reveals that the joint covertness constraint imposes a linear trade-off between the senders throughput.
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 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 establish the fundamental limits of covert communication over quantum channels, focusing on both finite-dimensional classical-quantum (CQ) channels and the infinite-dimen\-sional lossy thermal-noise bosonic channel. For general memoryless CQ channels, we characterize when covert communication is possible and prove a square root law (SRL): at most Ln+o(n)L\sqrt{n} + o(\sqrt{n})Ln​+o(n​) bits can be reliably transmitted covertly over nnn uses of the channel where LLL is the channel-dependent covert capacity. We derive a single-letter expression for LLL and show that the required pre-shared secret key also scales as n\sqrt{n}n​ under mild conditions. We also identify and characterize corner cases where either constant-rate or zero-rate covert communication is possible. For the bosonic channel, we prove that the SRL holds and derive exact covert capacities under different resource assumptions. In particular, we show that the covert secrecy and covert entanglement generation capacities both equal the covert classical capacity without entanglement-assistance, Lno-EAL_{\text{no-EA}}Lno-EA​, and show that the required pre-shared classical secret key scales as n\sqrt{n}n​. We also find that quadrature phase-shift keying (QPSK) achieves the optimal covert capacity, outperforming binary modulation in contrast to the classical channel setting. When Alice and Bob instead share entanglement, the covert classical capacity improves to LEAnlog⁡n+o(nlog⁡n)L_{\text{EA}} \sqrt{n} \log n + o(\sqrt{n} \log n)LEA​n​logn+o(n​logn), though this scaling is sensitive to noise in the entangled resource. Finally, we propose a practical covert transceiver and simulate its performance compared to recently experimentally-tested transceivers under realistic conditions.
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 thatO(n)O(\sqrt {n})O(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 toO(nlog⁡n)O(\sqrt {n}\log {n})O(n​logn)for continuous-variable bosonic channels. Here, we present a finite-dimensional parallel, and show thatO(nlog⁡n)O(\sqrt {n}\log {n})O(n​logn)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 asO(1/n)O\left ({{{\scriptstyle \text {}^{\scriptstyle 1}}\hspace {-0.224em}/\hspace {-0.112em}{\scriptstyle \sqrt {n}}}}\right)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.