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Quantum Illumination for Stealth Target Detection: A Discrete-Qubit Toy Model on PKTron and IBM Quantum Hardware

Zuhair Ahmed

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Abstract Quantum illumination has been proposed as a theoretical route to detecting low-reflectivity targets, such as stealth aircraft, in high-background-noise environments where classical radar performance degrades. The protocol, as originally formulated (Lloyd, 2008; Tan et al., 2008), uses continuous-variable entangled light (two-mode squeezed vacuum) and a specific phase-sensitive joint receiver to achieve a theoretical detection advantage over classical illumination of matched energy, even though the entanglement itself does not survive the round trip through a lossy, noisy channel. This study investigates whether that advantage appears in a simpler, discrete-variable (qubit) toy model, of the kind commonly used for pedagogical intuition, implemented on PKTron and cross-checked on IBM Quantum hardware. A rigorously fair comparison was constructed in which an entangled Bell pair and a classically correlated (separable) mixture of matched initial correlation strength were each subjected to identical loss and background-noise channels, with detection performance assessed via the same joint correlation measurement (Z⊗Z expectation) in both cases. In PKTron simulation, the entangled probe showed a correlation separation between target-present and target-absent hypotheses of 0.0100 at zero background noise, decreasing to 0.0025 at high background noise, while the classically correlated probe showed a substantially larger separation, decreasing from 0.1000 to 0.0500 over the same range — indicating no entanglement advantage, and if anything, a disadvantage, in this discrete model. This qualitative finding was independently corroborated on IBM Quantum's ibm_kingston hardware, using natural qubit T1 relaxation (rather than an artificially injected noise parameter) as the loss channel: entangled correlation degraded to 54.5% of its initial value after 60 microseconds, compared to 77.7% retained by the classically correlated mixture over the same interval. These results indicate that the theoretical quantum illumination advantage does not straightforwardly emerge from a simple discrete-qubit correlation model, consistent with the broader understanding that the effect is specific to continuous-variable Gaussian states and phase-sensitive joint detection, and consistent with quantum illumination's status as a theoretical concept with no demonstrated range or signal-to-noise advantage over classical radar to date.

DOI
10.21203/rs.3.rs-10883885/v1

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Abstract Quantum illumination has been proposed as a theoretical route to detecting low-reflectivity targets, such as stealth aircraft, in high-background-noise environments where classical radar performance degrades. The protocol, as originally formulated (Lloyd, 2008; Tan et al., 2008), uses continuous-variable entangled light (two-mode squeezed vacuum) and a specific phase-sensitive joint receiver to achieve a theoretical detection advantage over classical illumination of matched energy, even though the entanglement itself does not survive the round trip through a lossy, noisy channel. This study investigates whether that advantage appears in a simpler, discrete-variable (qubit) toy model, of the kind commonly used for pedagogical intuition, implemented on PKTron and cross-checked on IBM Quantum hardware. A rigorously fair comparison was constructed in which an entangled Bell pair and a classically correlated (separable) mixture of matched initial correlation strength were each subjected to identical loss and background-noise channels, with detection performance assessed via the same joint correlation measurement (Z⊗Z expectation) in both cases. In PKTron simulation, the entangled probe showed a correlation separation between target-present and target-absent hypotheses of 0.0100 at zero background noise, decreasing to 0.0025 at high background noise, while the classically correlated probe showed a substantially larger separation, decreasing from 0.1000 to 0.0500 over the same range — indicating no entanglement advantage, and if anything, a disadvantage, in this discrete model. This qualitative finding was independently corroborated on IBM Quantum's ibm_kingston hardware, using natural qubit T1 relaxation (rather than an artificially injected noise parameter) as the loss channel: entangled correlation degraded to 54.5% of its initial value after 60 microseconds, compared to 77.7% retained by the classically correlated mixture over the same interval. These results indicate that the theoretical quantum illumination advantage does not straightforwardly emerge from a simple discrete-qubit correlation model, consistent with the broader understanding that the effect is specific to continuous-variable Gaussian states and phase-sensitive joint detection, and consistent with quantum illumination's status as a theoretical concept with no demonstrated range or signal-to-noise advantage over classical radar to date.
Quantum Radar! Check out what Wikipedia says about it: it might render stealth aircraft obsolete. Watch YouTube videos that purport to explain all about it. Read press reports in which China claims it field tested one in 2016. But is there any fire underneath all that smoke? This talk will answer that question by telling the story of “quantum illumination”, from its beginnings through recent theoretical and experimental results. Quantum illumination is the only quantum radar concept that has been proven, theoretically, to outperform all classical radars of the same transmitted energy in detecting a weakly-reflecting target that is embedded in strong background noise. It uses a source of quadrature-entangled signal and idler beams to gain its target-detection performance improvement despite loss and noise that destroys the entanglement. A realistic assessment of that improvement's utility, however, shows that its value is severely limited. Nevertheless, the fact that entanglement can be of value on an entanglement-breaking channel — the meta-lesson of the quantum illumination story — should spur continued research on quantum radar.
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.
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.
Abstract To detect a stealth target, one may directly probe it with a single photon and analyze the reflected signals. The efficiency of such conventional detection scheme can potentially be enhanced by quantum illumination, where entanglement is exploited to break the classical limits. The question is what is the optimal signal state for achieving the detection limit? Here, we address this question in a general discrete model, and derive a complete set of analytic solutions. For one-shot detection, the parameter space can be classified into three distinct regions, in the form of a “phase diagram” for both conventional and quantum illumination. Interestingly, whenever the reflectivity of the target is less than some critical value, all received signals become useless, which is true even if entangled resources are employed. However, there does exist a region where quantum illumination can provide advantages over conventional illumination; there, the optimal signal state is an entangled state with an entanglement spectrum inversely proportional to the spectrum of the environmental noise state and is, surprisingly, independent of the occurrence probability and the reflectivity of the object. The entanglement of the ideal probe state increases with the entropy of the environment; it becomes more entangled as the temperature of the environment increases. Finally, we show that the performance advantage cannot be fully characterized by any measure of quantum correlation, unless the environment is a complete mixed state.
Quantum illumination (QI) is an entanglement-based protocol for improving LiDAR/radar detection of unresolved targets beyond what a classical LiDAR/radar of the same average transmitted energy can do. Originally proposed by Seth Lloyd as a discrete-variable quantum LiDAR, it was soon shown that his proposal offered no quantum advantage over its best classical competitor. Continuous-variable, specifically Gaussian-state, QI has been shown to offer a true quantum advantage, both in theory and in table-top experiments. Moreover, despite its considerable drawbacks, the microwave version of Gaussian-state QI continues to attract research attention. A recent QI study by Armanpreet Pannu, Amr Helmy, and Hesham El Gamal (PHE), however, has: (i) combined the entangled state from Lloyd’s QI with the channel models from Gaussian-state QI; (ii) proposed a new positive operator-valued measurement for that composite setup; and (iii) claimed that, unlike Gaussian-state QI, PHE QI achieves the Nair–Gu lower bound on QI target-detection error probability at all noise brightnesses. PHE’s analysis was asymptotic, i.e., it presumed infinite-dimensional entanglement. The current paper works out the finite-dimensional performance of PHE QI. It shows that there is a threshold value for the entangled-state dimensionality below which there is no quantum advantage, and above which the Nair–Gu bound is approached asymptotically. Moreover, with both systems operating with error-probability exponents 1 dB lower than the Nair–Gu bound, PHE QI requires enormously higher entangled-state dimensionality than does Gaussian-state QI to achieve useful error probabilities in both high-brightness (100 photons/mode) and moderate-brightness (1 photon/mode) noise. Furthermore, neither system has an appreciable quantum advantage in low-brightness (much less than 1 photon/mode) noise.
Quantum illumination and quantum entanglement provide an efficient method for detecting low-reflectivity targets in bright thermal-noise environments. Until now, almost all studies on quantum illumination assume that a target has only two mutually exclusive choices of being present and absent. In this study, we investigate the performance of quantum illumination when a target adopts a probabilistic mixed strategy. Remarkably, we show that the probabilistic mixed strategy can help the target hide its presence. This conclusion holds for asymptotic quantum illumination with joint measurement and practical quantum illumination with mode-by-mode local measurement. We also verify our result for Gaussian quantum illumination with a two-mode squeezed vacuum state and non-Gaussian quantum illumination with the NOON state. The mixed strategy is successful because of the large amount of resources consumed in target detection. This work is the next step toward better understanding of the stealth technique in future quantum illumination.