Experimental Quantum Target Detection Approaching the Fundamental Helstrom Limit

Feixiang Xu, Xiao-Ming Zhang, Liang Xu, Tao Jiang, Man-Hong Yung, and Lijian Zhang

Phys. Rev. Lett. 127, 040504 – Published 22 July 2021

Abstract

Quantum target detection is an emerging application that utilizes entanglement to enhance the sensing of the presence of an object. Although several experimental demonstrations for certain situations have been reported recently, the single-shot detection limit imposed by the Helstrom limit has not been reached because of the unknown optimum measurements. Here we report an experimental demonstration of quantum target detection, also known as quantum illumination, in the single-photon limit. In our experiment, one photon of the maximally entangled photon pair is employed as the probe signal and the corresponding optimum measurement is implemented at the receiver. We explore the detection problem in different regions of the parameter space and verify that the quantum advantage exists even in a forbidden region of the conventional illumination, where all classical schemes become useless. Our results indicate that quantum illumination breaks the classical limit for up to 40%, while approaching the quantum limit imposed by the Helstrom limit. These results not only demonstrate the advantage of quantum illumination, but also manifest its valuable potential of target detection.

Received 17 January 2021
Accepted 23 June 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.040504

Physics Subject Headings (PhySH)

Quantum channels Quantum sensing

General PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Feixiang Xu^1,2, Xiao-Ming Zhang³, Liang Xu^1,2, Tao Jiang^1,2, Man-Hong Yung^4,5,6,7,*, and Lijian Zhang ^1,2,†

¹National Laboratory of Solid State Microstructures, College of Engineering and Applied Sciences and School of Physics, Nanjing University, Nanjing 210093, China
²Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
³Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR, China
⁴Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
⁵Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
⁶Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
⁷Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China

^*yung@sustech.edu.cn
^†lijian.zhang@nju.edu.cn

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Issue

Vol. 127, Iss. 4 — 23 July 2021

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Images

Figure 1
A schematic of (a) conventional and (b) quantum illumination. In conventional illumination (a), a single photon as a probe signal state is sent to a suspected background noise region. An optimum positive operator-valued measure (POVM) is designed to detect the potential object. In quantum illumination (b), a pair of entangled photons is prepared, one of which (the idler) is directly sent to the receiver. The other one (the signal) is sent to the suspected region for illumination. A joint measurement is implemented at the receiver to detect the potential object.
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Figure 2
Experimental setup. (a) Conventional illumination: the signal is a heralded single photon, which is sent into port 1 of the target for illumination. After combination with the background noise from port 2, the output of port 3 is sent to the projective measurement for deciding the absence or presence of the target. (b) Quantum illumination: the heralded single photon is replaced with a photon entangled with an idler, which is sent to the Bell state measurement (BSM) directly. The signal is combined with the background noise and the output of port 3 is sent to the BSM for the joint measurement with the idler. (c) Target: a Sagnac interferometer–based polarization-independent beam splitter with tunable reflectivity. Key elements included half wave plate (HWP), PBS (polarizing beam splitter), 3 nm (3 nm bandpass filter), QP (quartz plate), NPBS (nonpolarizing beam splitter), APD (avalanche photodiode).
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Figure 3
Phase diagram for quantum illumination. The black solid lines denote the boundaries between different regions. The black dashed line represents the boundary between region II and region III of conventional illumination in the quantum illumination phase diagram for comparison. The table below the phase diagram shows the range of the three regions and their minimum error probabilities, where $η = R^{2} / [R^{2} + (1 - R)^{2}]$ .
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Figure 4
Experimentally measured error probabilities of conventional (red dots with error bars) and quantum (blue asterisks with error bars) illuminations for different prior probabilities (a) $p_{0} = 0.4$ , (b) $p_{0} = 0.5$ , (c) $p_{0} = 0.6$ , (d) $p_{0} = 0.7$ . The theoretical classical and quantum limit are shown as red dotted lines and black solid lines, respectively. The theoretical error probabilities for quantum illumination utilizing the state generated in the experiment are depicted as the blue dashed lines.
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Figure 5
Mutual information of quantum and conventional illumination and their difference (inset). The red solid line and the blue dashed line indicate the theoretical mutual information of conventional $I_{c}$ and quantum $I_{q}$ illumination utilizing the state generated from the experiment with respect to $p_{0} = 0.5$ . The red dots and blue asterisks with error bars are their corresponding experimental results. The inset shows the difference of the mutual information.
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