Chernoff Information Bottleneck for Covert Quantum Target Sensing

TL;DR

This work introduces a Chernoff information bottleneck framework to quantify covert quantum sensing under an energy constraint, defining the covert information curve $I_C(d,\mathcal{S})$ to trade off Alice's sensing rate $\xi^{(A)}$ against Eve's detection rate $\xi^{(E)}$. It demonstrates that entangled probes, specifically a collection of two-mode squeezed vacuum states, achieve sublinear scaling ($\gamma<1$) in the small-signal regime, enabling efficient covert target ranging with many modes $M$, while classical coherent probes exhibit linear scaling ($\gamma\approx1$) and cannot reach covert operation under the same constraints. The analysis provides analytical approximations for Chernoff informations in background-dominated optical scenarios and shows a practical path to integrating quantum sensing into LiDAR/Radar systems for secure, low-probability-of-detection operations. Overall, the paper identifies a clear quantum advantage in covert sensing and offers a concrete information-theoretic criterion for assessing covert performance in realistic optical settings.

Abstract

The paradigm of quantum metrology and sensing aims to identify a quantum advantage in precision at a fixed energy of the probe state. However, in practice, employing high-energy classical probes is often simpler than leveraging the quantum regime. This is not the case of covert sensing scenarios, where detection must be performed while avoiding to be discovered by an adversary, because increasing energy unduly facilitates the adversary. In this paper, we introduce a general framework to assess the quantum advantage in covert situations based on extending the information bottleneck principle to decision problems via the Chernoff information. We demonstrate how entangled photonic probes paired with photon counting significantly outperform classical coherent transmitters in covert detection and ranging, often representing the only option for secrecy. Thus, our work highlights the great potential of integrating quantum sensing into LiDAR and Radar systems to enhance covert performance.

Figures (4)

• Figure 1: Ranging and detention schemes. A. Ranging is performed by Alice that sends a probe returning in one of $m$ possible slots denoting different positions of the target. A decision is made after measuring the returning signal jointly with the unavoidable background noise. B. The covert sensing is performed by assuming that all (up to the collection efficiency) the signal that does not return is collected by an adversary performing passive measurement to detect Alice.
• Figure 2: Sensing-covertness trade-off. We plot the pair $\{\xi^{(E)},\xi^{(A)}\}$ for the TMSV (blue) and coherent (red) probe. The dashed orange line represents $\xi_{coh}^{(A,\infty)}$, characterizing the alternative classical strategy described in the End matter. The gray area denotes the region in which effective covertness (see main text) is allowed. The blue and red regions denote quantum and classical achievable sensing respectively. For panel A we set $\kappa =0.3, \mu_B=10, \eta_A=\eta_E=1$. For panel B$\kappa =0.2, \mu_B=1, \eta_A=1$ and $\eta_E=1$.
• Figure 3: A. Chernoff information scaling. We plot the parameter $\gamma$, defined in the main text, for the quantum probe as a function of the mean number of signal photons $\mu$ at different values of background. The parameters are $\kappa =0.2, \eta_A=1$ and $\eta_E=1$. B. Asymptotic probabilities of error. Asymptotic probabilities of error (in log scale) in the limit of a large number of modes $M$. The parameters are the same of panel A and we fix $\mu_B=10$ and $\mu=0.001$.
• Figure 4: A. We plot the scaling parameter $\gamma$ as a function of $\mu/\mu_B$ (with fixed $\mu=0.01$). The parameters are the same of Fig.(\ref{['fig:3']}), with either $\eta_E=1$ (solid lines), or $\eta_E=0.3$ (dashed lines). B. Asymptotic probabilities of error (in log scale) with $\eta_E=0.3$ and the other parameters as Fig.(\ref{['fig:3']}). The insert it's a magnification to show the separate scaling of $p^{(E)}$ and $p^{(A)}_{coh}$.