We report that shared entanglement improves the scaling law for quantum-secure covert communication over the thermal noise lossy bosonic channel and that our entanglement-assisted optical transceiver architecture captures this improvement.
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) 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)) for continuous-variable bosonic channels. Here, we present a finite-dimensional parallel, and show that O(nlog(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/n).
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)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(nlogn)for continuous-variable bosonic channels. Here, we present a finite-dimensional parallel, and show thatO(nlogn)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).
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) 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(nlogn) for continuous-variable bosonic channels. Here, we present a finite-dimensional parallel, and show that O(nlogn) covert bits can be transmitted reliably over n uses of a qubit depolarizing channel.
We revisit the problem of entanglement-assisted covert communication over bosonic channels and show that thebenefitsof entanglement can be achieved with fewer entanglement resources than previously identified. Specifically, we show thatO(nlogn)covert and reliable bits can be exchanged usingω(n)∩o(n)Two-Mode Squeezed-Vacuum (TMSV) pairs andω(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 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) bits can be reliably transmitted covertly over n uses of the channel where L is the channel-dependent covert capacity. We derive a single-letter expression for L and show that the required pre-shared secret key also scales as 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-EA, and show that the required pre-shared classical secret key scales as 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 LEAnlogn+o(nlogn), 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.