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 discovery by an adversary, because increasing energy unduly facilitates the adversary. In this Letter, 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.
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 discovery by an adversary, because increasing energy unduly facilitates the adversary. In this Letter, 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.
This thesis presents three studies in quantum-enhanced sensing and target detection. The first study explores covert target detection using optical or microwave probes, establishing quantum-mechanical limits on the error probabilities of entanglement-assisted detection methods while maintaining the sender's covertness. It identifies the minimal energy required to preserve covertness and reduce error probabilities, compares two-mode squeezed vacuum probes and coherent states against these limits, and extends the analysis to discriminating thermal loss channels and non-adversarial quantum illumination. The second study focuses on phase-insensitive optical amplifiers, determining the quantum limit on the precision of gain estimation using multimode probes possibly entangled with ancillary systems. It finds that the average photon number and the number of input modes are interchangeable resources for achieving optimal gain sensing precision, contrasting classical probes with quantum probes and highlighting the advantages of the latter, even with single-photon inputs and inefficient photodetection. It also provides a closed-form expression for the energy-constrained Bures distance between two amplifier channels. The third study compares three probe states -- coherent state, two-mode squeezed vacuum (TMSV), and single-photon entangled state (SPES) -- in quantum-enhanced target detection, assessing their performance under signal energy constraints relevant to covert radar sensing. SPES is uniquely positioned as a practical probe due to its non-classical properties after thermal loss and ease of generation. Numerical analysis shows that at low signal energies, the error exponent of TMSV aligns with SPES, indicating comparable detection capabilities and that SPES surpasses the best classical state-the coherent state-in accuracy for certain signal strengths.
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 O(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 O(ε) and O(M)+O(εM)+O(ε), respectively. In particular, in the strong covertness regime ε→0, the GCS CCQFI vanishes, whereas the TMSV retains a finite 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.
The laws of quantum physics endow superior performance and security for information processing: quantum sensing harnesses nonclassical resources to enable measurement precision unmatched by classical sensing, whereas quantum cryptography aims to unconditionally protect the secrecy of the processed information. Here, we present the theory and experiment for entanglement-enhanced covert sensing, a paradigm that simultaneously offers high measurement precision and data integrity by concealing the probe signal in an ambient noise background so that the execution of the protocol is undetectable with a high probability. We show that entanglement offers a performance boost in estimating the imparted phase by a probed object, as compared to a classical protocol at the same covertness level. The implemented entanglement-enhanced covert sensing protocol operates close to the fundamental quantum limit by virtue of its near-optimum entanglement source and quantum receiver. Our work is expected to create ample opportunities for quantum information processing at unprecedented security and performance levels.
Quantum Lidar is a future technology that can mean different things to different people. To some it means detection and identification of classical-type lidar signals reflected from an illuminated target at or near the single photon level. This is facilitated by advances in semiconductor detector technology that allow highly efficient photocounting. To others it is more stringent, requiring exploitation of covertness associated with being essentially undetectable by the target in a thermal background, whilst allowing the lidar operator to filter her own signal from this noise. Again there is nothing specifically quantum about this. Any source that mimics of the energy rate per bandwidth seen by the illuminated object in the direction of the source can appear covert. In order to exploit quantum optics one can use inherent correlations, whether entangled or otherwise between light beams. Simple correlated optical beams can do this in two ways, perhaps by storing one beam as a reference and later performing correlated detection with the return signal in a phase sensitive manner. This is the “gold standard” for quantum lidar, but will be difficult outside of laboratory situations. In microscopy such phase control might be possible, or perhaps in the radio or microwave region for a quantum radar. Less challenging is a scenario in which an immediate local measurement of one beam conditions the beam sent to the target, allowing the return signal to be sifted from noise more easily. Here we will consider such a simple system, providing a range equation for a basic quantum lidar if it is to be operated covertly or openly. Open operation allows increased quantum signal brightness but also provides a quantum advantage, unspoofability – the lidar operator can in principle recognise their own return signal. We will also provide an analysis of quantum lidar detection based on quantum hypothesis testing and use this to perform Monte Carlo simulation of both target detections and false positive avoidance in a noisy background. The theory will be applied to experimental data.
A Doppler radar is a device that employs the Doppler effect to estimate the radial velocity of a moving target at a distance. Traditional radars are based on a classical description of the electromagnetic radiation, but in principle their performance can be improved employing entangled quantum probe states. For target detection, i.e. hypothesis testing, a quantum advantage exists even in the high-noise regime appropriate to describe microwave fields, a protocol known as quantum illumination. In this paper, we show a similar advantage also for a quantum Doppler radar operating in presence of thermal noise, whereas so far a quantum advantage was shown in the noiseless scenario or in lidars operating at optical frequencies with negligible thermal noise. Concretely, we quantify the radar performance in terms of the quantum Fisher information, which captures the ultimate precision allowed by quantum mechanics in the asymptotic regime. We compare a classical protocol based on coherent states with a quantum one that uses multimode states obtained from spontaneous parametric downconversion. To ensure a fair comparison we match the signal energy and pulse duration. We show that a 3dB advantage is possible in the regime of small number of signal photons and high thermal noise, even for low transmissivity.
Quantum light promises improved precision in optical remote sensing, but its practical advantage depends critically on whether nonclassical resources remain useful under realistic noise and experimentally accessible detection. This question becomes especially relevant for LiDAR systems, where a quantum advantage has been demonstrated for target detection and joint range-velocity estimation, but mostly under idealized conditions or simple noise models, such as optical loss and thermal background. A key open point is whether entanglement provides an operational advantage when the dominant disturbance is not independent noise, but structured interference across sensing modes. Here, we address this question by studying the joint estimation of target range and velocity with bright two-mode Gaussian probes and homodyne detection, comparing coherent, separable squeezed, and twin-beam states at a fixed resource budget. Our results reveal a hierarchy of quantum resources set by the noise structure: separable squeezing provides a robust advantage over coherent illumination under loss and thermal background, whereas twin-beam probes become superior under correlated jamming when the receiver is adaptively optimized. These results establish correlated noise as the operational regime in which entanglement provides a robustness advantage beyond local squeezing, opening a receiver-aware route to quantum-enhanced LiDAR in realistic and potentially adversarial environments.