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.
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.
Quantum illumination can be used to detect the low-reflectivity target hidden in strong background noise. All known results are based on the assumption of ideal photon transmission and reception. In this paper, we investigate the impact of photon loss on the performance of quantum illumination in two distinct scenarios: (I) the probabilistic loss mode and (II) the hybrid loss model. In both scenarios it is shown that quantum illumination with bipartite entanglement outperforms its classic correspondence with coherent states in both error probability and its response to probabilistic photon loss. Moreover, in scenario I, the resource required in quantum illumination scales far less than 1/pch2 to completely compensate the channel efficiency pch2. This poses a sharp contrast with the consumption of classic illumination which scales as $\ensuremath{\gg}1/{p}_{\mathrm{ch}}^{2}$. However in scenario II, both quantum illumination and classic illumination need resources of more than 1/pch2, due to extra thermal noise introduced in the hybrid loss model.
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.
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.
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 illumination is a protocol where quantum resources are utilized to detect a low-reflectivity object embedded in a bright thermal noise bath. For example, quantum illumination with a two-mode squeezed state (TMSS) provides a 6 dB advantage in the error-probability exponent over the optimal classical illumination. We here consider quantum illumination with the photon-subtracted two-mode squeezed state (PSTMSS). Our result is twofold. First, we show that a much smaller error probability Perr could be obtained, meaning that much smaller resources will be required in quantum illumination for a fixed Perr. Second, quantum illumination with PSTMSS appreciably outperforms its classic correspondence in both low- and high-noise operating regimes, extending the regimes in which quantum illumination is optimal for target detection.
Quantum illumination is a technique for detecting the presence of a target in a noisy environment by means of a quantum probe. We prove that the two-mode squeezed vacuum state is the optimal probe for quantum illumination in the scenario of asymmetric discrimination, where the goal is to minimize the decay rate of the probability of a false positive with a given probability of a false negative. Quantum illumination with two-mode squeezed vacuum states offers a 6 dB advantage in the error probability exponent compared to illumination with coherent states. Whether more advanced quantum illumination strategies may offer further improvements had been a longstanding open question. Our fundamental result proves that nothing can be gained by considering more exotic quantum states, such as, e.g., multimode entangled states. Our proof is based on a fundamental entropic inequality for the noisy quantum Gaussian attenuators. We also prove that without access to a quantum memory, the optimal probes for quantum illumination are the coherent states.