Fundamental Limits of Covert Communication and Entanglement Generation over Quantum Channels

Abstract

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 $L\sqrt{n} + o(\sqrt{n})$ 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 $\sqrt{n}$ 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, $L_{\text{no-EA}}$, and show that the required pre-shared classical secret key scales as $\sqrt{n}$. 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 $L_{\text{EA}} \sqrt{n} \log n + o(\sqrt{n} \log n)$, 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.