Covert Signaling for Communication and Sensing over the Bosonic Channels

2026-05-08

AI Summary

This study investigates communication and active sensing strategies over lossy thermal-noise bosonic channels that jointly ensure covertness and practical compatibility. Addressing the square-root law constraint, the work proposes a sparse signaling scheme wherein constant-power signals are transmitted in only approximately √n channel uses, with silence otherwise maintained. Leveraging quantum information theory and bosonic channel modeling, it is rigorously shown that the optimal covert input state is a mixture of two adjacent photon-number states—specifically, the vacuum and single-photon states at low brightness. This result not only elucidates the fundamental trade-off between covertness and performance but also precisely characterizes the structure of the optimal state under minimal detectability and identifies the power threshold at which the system transitions from covertness-prioritized to performance-prioritized operation.

Abstract

Preventing signal detection in communication and active sensing requires careful control of transmission power. In fact, the square-root laws (SRL) for covert classical and quantum communication and sensing prescribe that the average output power per channel use scales as $1/\sqrt{n}$ for $n$ channel uses. Two strategies for achieving this are diffuse and sparse signaling. The former transmits signals with power decaying as $1/\sqrt{n}$ on all $n$ channel uses, which is convenient for mathematical analysis. The latter transmits constant-power signals rarely, on approximately $\sqrt{n}$ out of $n$ channel uses, while remaining silent on the others. This offers significant practical advantages in compatibility with modern digital transmitters. Here, we study sparse signaling over lossy thermal-noise bosonic channels, which describe quantumly many practical channels (including optical, microwave, and radio-frequency). We characterize the input signal state that minimizes detectability. We find an unintuitive optimal quantum state structure: a mixture of just two consecutive photon-number states. In particular, in the low-brightness regime, the optimal signal state is a mixture of vacuum and a single photon. Since these states are generally suboptimal for both communication and active sensing, we explore the resulting trade-off and identify input-power thresholds for transitions between optimizing for covertness vs. performance in communication and sensing tasks.

Problem

• covert signaling
• bosonic channels
• sparse signaling
• quantum communication
• active sensing

Innovation

• covert signaling
• sparse signaling
• bosonic channels
• quantum state optimization
• square-root law