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arXiv:2308.07150 · Physical Review A

Relation between quantum illumination and quantum parameter estimation

Wei Zhong, Dong-Qing Wang, Wenyi Zhu, Lan Zhou, Ming‐Ming Du, Yu‐Bo Sheng

Published May 22, 2025• 2 citations
arXivHTMLPDF

Abstract

Quantum illumination (QI) leverages entangled lights to detect the presence of low-reflectivity objects within a thermal environment. In a related vein, quantum parameter estimation utilizes nonclassical probes to precisely determine unknown system parameters. Although both fields have been studied extensively, their performances have traditionally been assessed using different figures of merit: signal-to-noise ratio for QI and quantum Fisher information for parameter estimation. In this paper, we reveal the intrinsic connection between these two measures in the context of target detection, thereby providing explicit operational criteria for identifying optimal measurements. We further apply this relationship to various target detection protocols that employ exotic non-Gaussian states derived from coherent states and two-mode squeezed vacuum states.

DOI
10.1103/physreva.111.052440

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Quantum illumination (QI) leverages entangled lights to detect the presence of low-reflectivity objects within a thermal environment. In a related vein, quantum parameter estimation utilizes nonclassical probes to precisely determine unknown system parameters. Although both fields have been studied extensively, their performances have traditionally been assessed using different figures of merit: signal-to-noise ratio for QI and quantum Fisher information for parameter estimation. In this paper, we reveal the intrinsic connection between these two measures in the context of target detection, thereby providing explicit operational criteria for identifying optimal measurements. We further apply this relationship to various target detection protocols that employ exotic non-Gaussian states derived from coherent states and two-mode squeezed vacuum states.
Quantum illumination consists in shining quantum light on a target region immersed in a bright thermal bath with the aim of detecting the presence of a possible low-reflective object. If the signal is entangled with the receiver, then a suitable choice of the measurement offers a gain with respect to the optimal classical protocol employing coherent states. Here, we tackle this detection problem by using quantum estimation techniques to measure the reflectivity parameter of the object, showing an enhancement in the signal-to-noise ratio up to 3 dB with respect to the classical case when implementing only local measurements. Our approach employs the quantum Fisher information to provide an upper bound for the error probability, supplies the concrete estimator saturating the bound, and extends the quantum illumination protocol to non-Gaussian states. As an example, we show how Schrödinger's cat states may be used for quantum illumination.
In quantum illumination (QI), a signal beam initially entangled with an idler beam held at the receiver interrogates a target region bathed in thermal background light. The returned beam is measured jointly with the idler in order to determine whether a weakly reflecting target is present. Using tools from quantum information theory, we derive lower bounds on the average error probability of detecting both specular and fading targets and on the mean squared error of estimating the reflectance of a detected target, which are obeyed by any QI transmitter satisfying a signal energy constraint. For bright thermal backgrounds, we show that the QI system using multiple copies of low-brightness two-mode squeezed vacuum states is nearly optimal. More generally, our results place limits on the best possible performance achievable using QI systems at all wavelengths, and at all signal and background noise levels.
Quantum-enhanced sensing has a goal of enhancing a parameter sensitivity with input quantum states, while quantum illumination has a goal of enhancing a target detection capability with input entangled states in a heavy noise environment. Here we propose a concatenation between quantum-enhanced sensing and quantum illumination that can take quantum advantage over the classical limit. First, phase sensing in an interferometry is connected to a target sensing via quantum Fisher information. Second, the target sensitivity is investigated in noisy quantum-enhanced sensing. Under the same input state energy, for example, NNN-photon entangled states can exhibit better performance than a two-mode squeezed vacuum state and a separable coherent state. Incorporating a photon-number difference measurement, finally, the noisy target sensitivity is connected to a signal-to-noise ratio which is associated with a minimum error probability of discriminating the presence and absence of the target. We show that both the target sensitivity and the signal-to-noise ratio can be enhanced with increasing thermal noise.
Quantum illumination (QI) exploits quantum correlations to detect weakly reflecting targets embedded in noisy environments with higher sensitivity than classical illumination (CI). We investigate the effectiveness of QI in a realistic setting in which the signal sequentially interacts with a noisy environment and a lossy target. The target is considered at a temperature distinct from its surroundings, while both the interactions are modeled as an action of independent beam splitters with different reflectivities. The detection performance is quantified using the signal-to-noise ratio (SNR) and the quantum Chernoff bound (QCB), the latter providing an upper bound on the error probability. The performance of the Gaussian two-mode squeezed state (TMSS) is compared with that of the optimal classical protocol based on coherent states (CS). The proposed model shows that TMSS consistently achieves a higher SNR than CS for a low-reflectivity target and an arbitrary phase change and remains robust against thermal noise. Furthermore, a sufficiently lower QCB is obtained for TMSS than in previously reported results, indicating greater distinguishability between the presence and absence of the target. These findings underscore the role of realistic modeling in improving QI-based detection of lossy targets, with potential relevance to quantum radar and lidar systems.
Quantum illumination is a quantum sensing protocol primarily used for object detection, which aims to detect the presence of a target with low reflectivity in the free space using quantum light fields. Here we investigate a quantum illumination scheme using an entangled light source by performing non-Gaussian operations on the two-mode squeezed vacuum (TMSV) state in order to reduce the detection error probability and meanwhile improve the signal-to-noise (SNR) ratio. We demonstrate that under the same squeezing parameter, the non-Gaussian operations can significantly reduce the detection error rate compared with the original TMSV state. Under the same average signal photon number, both the TMSV states with and without non-Gaussian operations can provide smaller error rate than that of the coherent state. In addition, we consider the balanced homodyne detection on idler and return signal photons as joint measurement and find that non-Gaussian operations can enhance the SNR of target detection by about 6--9 dB compared with that using TMSV. These results here demonstrate the advantage of the non-Gaussian entangled source in quantum illumination protocol and can find potential applications in target detection in noisy environment.
There has been a great interest in quantum metrology (e.g., quantum interferometric radar) due to its applications in sub-Rayleigh ranging and remote sensing. Despite interferometric radar has received vast amount of attentions over the past two decades, very few researches has been conducted on another type of quantum radar: quantum illumination radar, or more precisely quantum target detection. It is, in general, used to interrogate whether the low-reflectivity target in a noisy thermal bath is existed using quantum light. The entanglement properties of its emitted light source give it a unique detection advantage over the classical radar. Entangled coherent state (ECS), as a class of quantum states with high entanglement robustness in noisy environments, has been widely used in several fields of quantum science such as quantum informatics, quantum metrology . In this paper, we investigate the target detection performance of quantum illumination radar based on three different types of ECS states. We employ the two-mode squeezed vacuum state (TMSV) and the coherent state as benchmarks to compare and analyze the relationship between the entanglement strength of the three types of ECS states and their quantum illumination detection performance. We found that the detection performance of the three ECS states is better than that of the coherent state. However, it is inferior to that of the TMSV state when the target is of low reflectivity. The emitted photon number is much smaller than the background noise (we call this as “good” illumination conditions). On the contrary, quantum illumination radar has no obvious advantage over coherent state radar for target detection under other illumination conditions; further, the detection performance of these three types of ECS states is not evidently related to that of the TMSV state and the coherent state. Finally, we reveal that the target detection performance of quantum illumination for the first two types of ECS states can be determined by their entanglement strength under “good” illumination conditions by adjusting the inter-modal phase of these two ECS states while keeping the emitted photon number constant. Under other illumination conditions, there is no evidence to demonstrate the entanglement strength of ECS states being associated with their target detection performance.