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Journal of Physics A Mathematical and Theoretical

Performance advantage of quantum illumination using symmetric and asymmetric hypothesis testings in lossy environments

Jiandong Zhang, Kaimin Zheng, B. G. Wang, Lijian Zhang

Published May 21, 2025• 1 citation
Publisher

Abstract

Abstract Quantum illumination is an emerging quantum technology that can detect whether a weakly reflecting target is present or absent in highly noisy environments. For practical purposes, in this paper we analyze the performance limit of a quantum illumination scheme and that of a classical illumination scheme in the presence of photon loss. The performance advantage of quantum illumination over classical illumination is addressed in settings of symmetric and asymmetric hypothesis testings. We analyze the effects of photon loss and discuss the relevant physical mechanisms. In addition, we demonstrate that noiseless linear amplification can be used to enhance the performance advantage. Our results are a foray into confirmation of the validity of quantum illumination and show more realistic performance advantage for practical applications.

DOI
10.1088/1751-8121/addb94

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Abstract Quantum illumination is an emerging quantum technology that can detect whether a weakly reflecting target is present or absent in highly noisy environments. For practical purposes, in this paper we analyze the performance limit of a quantum illumination scheme and that of a classical illumination scheme in the presence of photon loss. The performance advantage of quantum illumination over classical illumination is addressed in settings of symmetric and asymmetric hypothesis testings. We analyze the effects of photon loss and discuss the relevant physical mechanisms. In addition, we demonstrate that noiseless linear amplification can be used to enhance the performance advantage. Our results are a foray into confirmation of the validity of quantum illumination and show more realistic performance advantage for practical applications.
Abstract Quantum target detection aims to utilise quantum technologies to achieve performances in target detection not possible through purely classical means. Quantum illumination is an example of this, based on signal–idler entanglement, promising a potential 6 dB advantage in error exponent over its optimal classical counterpart. So far, receiver designs achieving this optimal reception remain elusive with many proposals based on Gaussian processes appearing unable to utilise quantum information contained within Gaussian state sources. This paper considers the employment of a noiseless linear amplifier at the detection stage of a quantum illumination-based quantum target detection protocol. Such a non-Gaussian amplifier offers a means of probabilistically amplifying an incoming signal without the addition of noise. Considering symmetric hypothesis testing, the quantum Chernoff bound is derived and limits on detection error probability is analysed for both the two-mode squeezed vacuum state and the coherent state classical benchmark. Our findings show that in such a scheme the potential quantum advantage is amplified even in regimes where quantum illumination alone offers no advantage, thereby extending its potential use. The same cannot be said for coherent states, whose performances are generally bounded by that without amplification.
Entanglement is arguably the key quantum-mechanical resource for improving the performance of communication, precision measurement and computing systems beyond their classical-physics limits. Yet entanglement is fragile, being very susceptible to destruction by the decoherence arising from loss and noise. Surprisingly, Lloyd (2008 Science 321 1463) recently proved that a very large performance gain accrues from use of entanglement in single-photon target detection within an entanglement-destroying lossy, noisy environment when compared to what can be achieved with unentangled single-photon states. We extend Lloyd's analysis to the full multiphoton input Hilbert space. We show that the performance of Lloyd's single-photon'quantum illumination' system is, at best, equal to that of a coherent-state transmitter of the same average photon number, and may be substantially worse. We demonstrate that the coherent-state system derives its advantage from the coherence between a sequence of weak—single photon on average—transmissions, a possibility that was not allowed for in Lloyd's work. Nevertheless, as shown by Tan et al (2008 Phys. Rev. Lett. 101 253601), quantum illumination may offer a significant, although more modest, performance gain when operation is not limited to the single-photon regime.
Entanglement is arguably the key quantum-mechanical resource for improving the performance of communication, precision measurement and computing systems beyond their classical-physics limits. Yet entanglement is fragile, being very susceptible to destruction by the decoherence arising from loss and noise. Surprisingly, Lloyd (2008 Science 321 1463) recently proved that a very large performance gain accrues from use of entanglement in single-photon target detection within an entanglement-destroying lossy, noisy environment when compared to what can be achieved with unentangled single-photon states. We extend Lloyd's analysis to the full multiphoton input Hilbert space. We show that the performance of Lloyd's single-photon'quantum illumination' system is, at best, equal to that of a coherent-state transmitter of the same average photon number, and may be substantially worse. We demonstrate that the coherent-state system derives its advantage from the coherence between a sequence of weak—single photon on average—transmissions, a possibility that was not allowed for in Lloyd's work. Nevertheless, as shown by Tan et al (2008 Phys. Rev. Lett. 101 253601), quantum illumination may offer a significant, although more modest, performance gain when operation is not limited to the single-photon regime.
Use of non-classical light in a quantum illumination scheme provides an advantage over classical illumination when used for LIDAR with a simple and realistic detection scheme based on Geiger-mode single photon detectors. Here we provide an analysis that accounts for the additional information gained when detectors do not fire that is typically neglected and show an improvement in performance of quantum illumination. Moreover, we provide a theoretical framework quantifying performance of both quantum and classical illumination for simple target detection, showing parameters for which a quantum advantage exists. Knowledge of the regimes that demonstrate a quantum advantage will inform where possible practical quantum LIDAR utilising non-classical light could be realised.
Quantum illumination is an idea for detection of targets in the presence of a noisy background using a photon pair that is entangled in some degree of freedom, such as frequency. This paper provides a simple and illustrative proof-of-concept setup of a quantum illumination investigation. Detection and imaging is investigated in the optical regime using a correlated source and the performance of classical illumination and quantum illumination are compared for detection and imaging experiments. The quantum advantage is demonstrated in the acquired data and possible application spaces and technological requirements are identified for developing practical systems.
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.