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IEEJ Transactions on Electronics Information and Systems

Simple Detection Scheme and Performance Evaluation for Quantum Illumination Using Quasi-Bell State

Tiancheng Wang, Tsuyoshi Sasaki Usuda

Published Nov 30, 2023• 1 citation
Publisher

Abstract

Quantum illumination has been a hot topic in quantum sensing since first proposed by S. Lloyd in 2008. Quantum illumination is an entanglement-based protocol that is able to detect the existence of a target in an environment with low-energy transmissivity and strong thermal noise. The Bell state and the two-mode squeezed vacuum (TMSV) state as an entangled light source have been widely discussed. In our previous study, we clarified that quantum illumination using the quasi-Bell state offers good performance at error probability even though easing the above-mentioned restrictions on the environment. In this study, we considered and discussed a physical implementation of a measurement scheme for the quasi-Bell state-based quantum illumination using a beam splitter and photon counters. As the result, although the measurement scheme is not an optimum scheme, it still offers a clear advantage over that using the TMSV state, which allows optimum quantum detection, under almost situations.

DOI
10.1541/ieejeiss.143.1090

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Quantum illumination has been a hot topic in quantum sensing since first proposed by S. Lloyd in 2008. Quantum illumination is an entanglement-based protocol that is able to detect the existence of a target in an environment with low-energy transmissivity and strong thermal noise. The Bell state and the two-mode squeezed vacuum (TMSV) state as an entangled light source have been widely discussed. In our previous study, we clarified that quantum illumination using the quasi-Bell state offers good performance at error probability even though easing the above-mentioned restrictions on the environment. In this study, we considered and discussed a physical implementation of a measurement scheme for the quasi-Bell state-based quantum illumination using a beam splitter and photon counters. As the result, although the measurement scheme is not an optimum scheme, it still offers a clear advantage over that using the TMSV state, which allows optimum quantum detection, under almost situations.
Quantum illumination is an entanglement-based protocol for target detection. The use of a two-mode squeezed vacuum (TMSV) state as a type of Gaussian state has been widely discussed. In our previous study, we found that the quasi-Bell state, which is a non-Gaussian state, outperforms the TMSV state in the quantum illumination protocol with attenuation. In this paper, we construct a detection scheme using practical elements and demonstrate that it can outperform the TMSV state without using the photon-number resolution.
Quantum illumination is one of the application protocols of This protocol uses entanglement for target detection. The protocol was first proposed by Lloyd, and its performance was later studied by Tan et al. In a lossy environment, they considered a Gaussian state in the presence of thermal noise. Entanglement with nonorthogonal states, such as coherent states, produces These states have been shown to be capable of perfect entanglement. In this paper, we consider quantum illumination using quasi-Bell states, and compute the minimum error probability of quantum illumination under these states.
Quantum illumination proposed by Lloyd is a protocol that detects the existence of a target by using entangled light of two-mode. Quantum illumination was first proposed using the Bell state, and then the use of a two-mode Gaussian state was proposed. On the other hand, there are many impact studies using the quasi-Bell state. However, as far as we know, there are no studies that analyze quantum illumination using the quasi-Bell state. Therefore, we focused on the performance evaluation of quantum illumination using the quasi-Bell state in this paper. We compared and considered the effects using the Bell state, the two-mode Gaussian state, the maximum quasi-Bell state, the non-maximum quasi-Bell state, and the coherent state (i.e., a laser radar) on the attenuated channel. In particular, we derived the exact solutions of the error probabilities when using the maximum and non-maximum quasi-Bell states. Then we clarified that quantum illumination using the quasi-Bell state offers a clear advantage over that using the other entangled states under almost situations and always offers a clear advantage over the laser radar.
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.
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{P}_{\mathrm{err}}Perr​ could be obtained, meaning that much smaller resources will be required in quantum illumination for a fixed Perr{P}_{\mathrm{err}}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.
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.