Covert Signaling for Communication and Sensing over the Bosonic Channels

TL;DR

This paper investigates sparse quantum signaling strategies over bosonic channels to optimize covert communication and sensing, revealing an optimal quantum state mixture that balances detectability and performance.

Contribution

It introduces a novel analysis of sparse signaling over bosonic channels, identifying an optimal two-state photon mixture for minimizing detectability.

Findings

Optimal input state is a mixture of two consecutive photon-number states.

In low-brightness regimes, the optimal state is a mixture of vacuum and single photon.

Thresholds are identified for transitioning between covertness and performance optimization.

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.