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Optics Continuum

Detection scheme using a beam splitter and on-off detectors for non-Gaussian state-based quantum illumination with attenuation

Tiancheng Wang, Tsuyoshi Sasaki Usuda

Published Mar 7, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1364/optcon.514321

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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 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.
Enhancing quantum illumination with highly entangled probes remains an active area of research. In this context, non-Gaussian operations provide an effective route for engineering probe states that can surpass the standard two-mode squeezed state (TMSS). In this work, we investigate a specific nonlocal non-Gaussian operation protocol and show that the engineered state using this protocol outperforms previously considered local non-Gaussian scenarios, engineered based on photon catalysis, addition, and subtraction under realistic conditions, including photon loss. Furthermore, by employing a 50:5050{:}5050:50 beam splitter with photon-number difference detection, we demonstrate a significant enhancement in the signal-to-noise ratio (SNR) for target detection relative to the TMSS. Thus, our protocol exhibits improved performance, highlighting a resource-efficient and experimentally feasible probe for enhanced 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.
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.
In a quantum illumination (QI) protocol, the task is to detect the presence of the target which is typically modelled by a partially reflecting beam splitter. We analyze the performance of QI when the target absorbs part of the light that falls on it, thereby making the scenario more realistic. We present an optical setup that models a target with these characteristics and explore its detectability in the quantum domain in terms of the Chernoff bound (CB). For an idler-free setup, we use the coherent state for QI while the two mode squeezed vacuum (TMSV) state is employed in the signal-idler scheme. In both the cases, we report an absorption-induced enhancement of the detection efficiency indicated by a lowering of CB with increasing amounts of absorption. Interestingly, we show that in the presence of absorption, a more intense thermal background can lead to target detection with enhanced efficiency. Moreover, we observe that the quantum advantage persists even for finite amounts of absorption. However, we find that the quantum advantage offered by TMSV decreases monotonically with absorption, and becomes vanishingly small in the high absorption regime. We also demonstrate the optimality of both the coherent and the TMSV states in their respective setups (idler-free and signal-idler) in the limit of low reflectivity and absorption.
It is important to find feasible measurement bounds for quantum information protocols. We present analytic bounds for quantum illumination with Gaussian states when using an on-off detection or a photon number resolving (PNR) detection, where its performance is evaluated with signal-to-noise ratio. First, for coincidence counting measurement, the best performance is given by the two-mode squeezed vacuum (TMSV) state which outperforms the coherent state and the classically correlated thermal (CCT) state. However, the coherent state can beat the TMSV state with increasing signal mean photon number in the case of the on-off detection. Second, the performance is enhanced by taking Fisher information approach with all counting probabilities including non-detection events. In the Fisher information approach, the TMSV state still presents the best performance but the CCT state can beat the TMSV state with increasing signal mean photon number in the case of the on-off detection. Furthermore, we show that it is useful to take the PNR detection on the signal mode and the on-off detection on the idler mode, which reaches similar performance of using PNR detection on both modes.