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Physical Review A

Quantum illumination in the presence of photon loss

ShengLi Zhang, Xu‐Bo Zou, Jianhong Shi, Jiansheng Guo, Guang‐Can Guo

Published Nov 6, 2014• 24 citations
Publisher

Abstract

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 $1/{p}_{\mathrm{ch}}^{2}$ to completely compensate the channel efficiency ${p}_{\mathrm{ch}}^{2}$. 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 $1/{p}_{\mathrm{ch}}^{2}$, due to extra thermal noise introduced in the hybrid loss model.

DOI
10.1103/physreva.90.052308

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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/pch21/{p}_{\mathrm{ch}}^{2}1/pch2​ to completely compensate the channel efficiency pch2{p}_{\mathrm{ch}}^{2}pch2​. This poses a sharp contrast with the consumption of classic illumination which scales as \ensuremath≫1/pch2\ensuremath{\gg}1/{p}_{\mathrm{ch}}^{2}\ensuremath≫1/pch2​. However in scenario II, both quantum illumination and classic illumination need resources of more than 1/pch21/{p}_{\mathrm{ch}}^{2}1/pch2​, due to extra thermal noise introduced in the hybrid loss model.
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.
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 (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.
We report the quantum-enhanced metal target detection based on quantum illumination, and experimentally verified that quantum illumination still helps low-reflectivity target detection in photon loss scenarios. The results show that the signal-to-noise ratio and target recognition ability of the quantum detection system are more than 10 times stronger than those of the classical detection under the same thermal noise conditions. We believe that the photon-counting based QI protocol, for its robustness to noise and losses, has a huge potentiality to promote the usage of quantum correlated light in real environments.
In quantum illumination, the probe and idler photons are entangled, and both are jointly measured at the end. The entanglement between the probe and idler photons enhances the detection performance per unit average photon number in the probe mode, particularly in low-reflectivity and high-noise scenarios. However, photon loss degrades the absolute detection performance and progressively reduces the performance gain relative to optimal classical strategies by diminishing non-classical correlations. To address this, we employ a channel superposition framework that encompasses two types of channel superposition protocols: indefinite causal order (ICO) and path superposition with a disjoint environment (PS-DE). Under the effective erasure/fading loss model adopted for the low-brightness regime, our analytical and numerical analysis based on the quantum Chernoff bound shows that both ICO and PS-DE can, in principle, achieve an advantage. The advantage persists as long as non-zero interference remains, reverting to the performance of standard quantum illumination once the interference is completely suppressed. Crucially, within this model, the ICO protocol is significantly more robust, maintaining a tighter upper bound on the error probability than standard quantum illumination and the PS-DE approach. This performance hierarchy is rooted in their fundamental structures: ICO exploits a shared environment to generate stronger quantum interference, while PS-DE, relying on disjoint environments, offers a more experimentally tractable, albeit weaker, alternative.
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.