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Physical Review A

Quantum illumination with photon-subtracted continuous-variable entanglement

ShengLi Zhang, Jiansheng Guo, Wan‐Su Bao, Jianhong Shi, Chenhui Jin, Xu‐Bo Zou, Guang‐Can Guo

Published Jun 9, 2014• 68 citations
Publisher

Abstract

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 ${P}_{\mathrm{err}}$ could be obtained, meaning that much smaller resources will be required in quantum illumination for a fixed ${P}_{\mathrm{err}}$. 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.

DOI
10.1103/physreva.89.062309

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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 takes advantage of quantum entanglement to achieve low error probability for detecting a low reflective object embedded in a noisy thermal bath. The two-mode squeezed state (TMSS), which is a Gaussian state, has been applied to quantum illumination as the detecting states in experiment. The photon-subtracted TMSS has also been proposed to achieve even lower error probability. Here we study quantum illumination with non-Gaussian states generated by photon subtraction and photon addition. Helstrom limit and quantum Chernoff bound are evaluated for comparison between performance of states with the same squeezing strength and with the same signal strength, respectively. Particularly, states generated by asymmetrical coherent superposition of photon subtraction and addition are studied, which are shown by us to have better performance than symmetrical ones. We show that non-Gaussian operations enhance the quantum illumination by introducing both stronger entanglement and signal strength. We then give a strategy on how to choose the optimal states for the best performance in different scenarios.
\n\tWe theoretically propose a quantum illumination receiver based on the ideal photon-subtracted two-mode squeezed state (PSTMSS) to efficiently detect the noise-hidden target. This receiver is generated by applying an optical parametric amplifier (OPA) to the cross correlation detection. With analyzing the output performance, it is found that OPA as a preposition technology of the receiver can contribute to the PSTMSS by significantly reducing the error probability than that of the general two-mode squeezed state (TMSS). Comparing with TMSS, the signal-to-noise ratio of quantum illumination based on ideal PSTMSS and OPA is improved more than 4 dB under an optimal gain of OPA. This work may provide a potential improvement in the application of accurate target detection when two kinds of resource have the identical real squeezing parameter.
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 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 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 $\ensuremath{\gg}1/{p}_{\mathrm{ch}}^{2}$. 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 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.