Covertness as a resource constraint in quantum target sensing

Abstract

Quantum covert target sensing aims to detect low-reflectivity targets embedded in the thermal environment while avoiding discovery by an adversary. This covertness requirement constrains the admissible probe energy, thereby imposing a trade-off between covertness and sensing performance. However, how this resource constraint determines the ultimate estimation precision of the target parameter remains largely unexplored. To fill this gap, we establish a unified framework connecting covert target discrimination with quantum-enhanced parameter estimation. We first present perturbative $ε$-covertness-induced bounds on the probe energy, which yield an admissible energy window narrowing as $\mathcal{O}(\sqrt{ε/M})$. Moreover, we introduce the covertness-constrained quantum Fisher information (CCQFI) to quantify the ultimate precision of target-reflectivity estimation and assess its attainability with specific measurements. For Gaussian-distributed coherent-state (GCS) and two-mode squeezed vacuum (TMSV) probes, their CCQFIs scale as $\mathcal{O}(ε)$ and $\mathcal{O}(M)+\mathcal{O}(\sqrt{εM})+\mathcal{O}(ε)$, respectively. In particular, in the strong covertness regime $ε\to0$, the GCS CCQFI vanishes, whereas the TMSV retains a finite $\mathcal{O}(M)$ contribution exhibiting a pronounced metrological advantage. Besides, photon counting saturates the GCS CCQFI, whereas homodyne detection achieves a higher attainability for the TMSV probe. Our work identifies covertness as a quantitative resource constraint governing the metrological limits of quantum target sensing.