Abstract
Quantum-enhanced receiver is an effective approach to discriminate weak coherent states with better performance. As a typical quantum-enhanced measurement scheme, Dolinar receivers theoretically approach the standard quantum limit by using real-time quantum feedback with optimal displacement and photon measurements. However, thermal noise can interfere with the results of photon measurement, ultimately leading to a degradation of performance. In this paper, we analyze the influence of thermal noise toward the detector and we build a more practical model of quantum-enhanced receiver with a replaced photon number resolving detector under thermal noise. The calculation model for decision strategy and displacement operator is optimized correspondingly by theoretical analysis to further improve the detection performance. This scheme provides an exact number of photons and accuracy calculation model of displacement operator and decision strategy, which reduce the degradation of performance caused by thermal noise. The simulation results show that the thermal noise causes a large interference with the quantum-enhanced measurements. The corrected scheme with the measurement model developed in this paper reduces the degradation of performance caused by thermal noise, and beats the standard quantum limit with the mean photon number of thermal noise less than 0.1. This work provides a meaningful step toward the performance enhancement of coherent state discrimination and enhances the capability for practical applications of quantum-enhanced measurement in coherent optical communications.





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Burenkov, I.A., Jabir, M.V., Polyakov, S.V.: Practical quantum-enhanced receivers for classical communication. AVS Quant. Sci. 3, 025301 (2021). https://doi.org/10.1116/5.0036959
Helstrom, C.W.: Quantum detection and estimation theory. J. Stat. Phys. 1, 231–252 (1969). https://doi.org/10.1007/BF01007479
Huttner, B., Imoto, N., Gisin, N., Mor, T.: Quantum cryptography with coherent states. Phys. Rev. A 51, 1863–1869 (1995). https://doi.org/10.1103/PhysRevA.51.1863
Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 3121–3124 (1992). https://doi.org/10.1103/PhysRevLett.68.3121
Cheng Jian, Feng Jin-Xia, Li Yuan-Ji, Zhang Kuan-Shou, 1. State key laboratory of quantum optics and quantum optics devices, institute of opto-electronics, Shanxi University, Taiyuan 030006, China;, 2. Collaborative Innovation center of extreme optics, Shanxi University, Taiyuan 030006, China: Measurement of low-frequency signal based on quantum-enhanced fiber Mach-Zehnder interferometer. Acta Phys. Sin. 67, 244202 (2018). https://doi.org/10.7498/aps.67.20181335
Li Shi-Yu, Tian Jian-Feng, Yang Chen, Zuo Guan-Hua, Zhang Yu-Chi, Zhang Tian-Cai, 1. Collaborative Innovation center of extreme optics, state key laboratory of quantum optics and quantum optics devices, institute of opto-electronics, Shanxi University, Taiyuan 030006, China;, 2. College of physics and electronic engineering, Shanxi University, Taiyuan 030006, China: effect of detection efficiency on phase sensitivity in quantum-enhanced Mach-Zehnder interferometer. Acta Phys. Sin. 67, 234202 (2018). https://doi.org/10.7498/aps.67.20181193
Heng-Xin, S., Kui, L., Jun-Xiang, Z., Jiang-Rui, G.: State key laboratory of quantum optics and quantum optics devices, institute of opto-electronics, Shanxi University, Taiyuan 030006, China: quantum precision measurement based on squeezed light. Acta Phys. Sin. 64, 234210 (2015). https://doi.org/10.7498/aps.64.234210
Bhadani, R., Djordjevic, I.B.: Constellation optimization for phase-shift keying coherent states with displacement receiver to maximize mutual information. IEEE Access. 8, 224409–224419 (2020). https://doi.org/10.1109/ACCESS.2020.3044086
Izumi, S., Neergaard-Nielsen, J.S., Andersen, U.L.: Adaptive generalized measurement for unambiguous state discrimination of quaternary phase-shift-keying coherent states. PRX Quant. 2, 020305 (2021). https://doi.org/10.1103/PRXQuantum.2.020305
Becerra, F.E., Fan, J., Baumgartner, G., Polyakov, S.V., Goldhar, J., Kosloski, J.T., Migdall, A.: M -ary-state phase-shift-keying discrimination below the homodyne limit. Phys. Rev. A 84, 062324 (2011). https://doi.org/10.1103/PhysRevA.84.062324
Li, K., Zhu, B.: Optimal partitioned-interval detection binary quantum receiver with practical devices. In: 2013 IEEE photonics society summer topical meeting series. pp. 167–168 (2013)
Vilnrotter, V.A.: Quantum receiver for distinguishing between binary coherent-state signals with partitioned-interval detection and constant-intensity local lasers. Interplanetary network progress report. 1–22 (2012)
Vilnrotter, V., Rodemich, E.: A generalization of the near-optimum binary coherent state receiver concept (Corresp.). IEEE Transact. Inform. Theory 30, 446–450 (1984). https://doi.org/10.1109/tit.1984.1056853
Izumi, S., Neergaard-Nielsen, J.S., Miki, S., Terai, H., Andersen, U.L.: Experimental demonstration of a quantum receiver beating the standard quantum limit at telecom wavelength. Phys. Rev. Appl. 13, 054015 (2020). https://doi.org/10.1103/PhysRevApplied.13.054015
Fang Xu, Mohammad-Ali Khalighi, Salah Bourennane: Impact of different noise sources on the performance of PIN- and APD-based FSO receivers. In: Proceedings of the 11th International Conference on Telecommunications. pp. 211–218 (2011)
Yuan, R., Zhao, M., Han, S., Cheng, J.: Kennedy receiver using threshold detection and optimized displacement under thermal noise. IEEE Commun. Lett. 24, 1313–1317 (2020). https://doi.org/10.1109/LCOMM.2020.2980537
Sych, D., Leuchs, G.: Practical receiver for optimal discrimination of binary coherent signals. Phys. Rev. Lett. 117, 200501 (2016). https://doi.org/10.1103/PhysRevLett.117.200501
Shcherbatenko, M.L., Elezov, M.S., Goltsman, G.N., Sych, D.V.: Sub-shot-noise-limited fiber-optic quantum receiver. Phys. Rev. A 101, 032306 (2020). https://doi.org/10.1103/PhysRevA.101.032306
Cariolaro, G., Pierobon, G.: Performance of quantum data transmission systems in the presence of thermal noise. IEEE Trans. Commun. 58, 8 (2010)
Izumi, S., Takeoka, M., Ema, K., Sasaki, M.: Quantum receivers with squeezing and photon-number-resolving detectors for M -ary coherent state discrimination. Phys. Rev. A 87, 042328 (2013). https://doi.org/10.1103/PhysRevA.87.042328
Li, K., Zuo, Y., Zhu, B.: Suppressing the errors due to mode mismatch for M-ary PSK quantum receivers by photon-number-resolving detector. IEEE Photonics Technol. Lett. 25, 2182–2184 (2013). https://doi.org/10.1109/LPT.2013.2282155
Becerra, F.E., Fan, J., Migdall, A.: Photon number resolution enables quantum receiver for realistic coherent optical communications. Nat. Photon. 9, 48–53 (2015). https://doi.org/10.1038/nphoton.2014.280
Elezov, M.S., Shcherbatenko, M.L., Sych, D.V., Goltsman, G.N.: Development of control method for an optimal quantum receiver. J. Phys. Conf. Ser. 1695, 012126 (2020). https://doi.org/10.1088/1742-6596/1695/1/012126
Vajente, G., Yang, L., Davenport, A., Fazio, M., Ananyeva, A., Zhang, L., Billingsley, G., Prasai, K., Markosyan, A., Bassiri, R., Fejer, M.M.: Low mechanical loss TiO2: GeO2 coatings for reduced thermal noise in gravitational wave interferometers. Phys. Rev. Lett. 127(7), 071101 (2021). https://doi.org/10.1103/PhysRevLett.127.071101
Kimble, H.J., Lev, B.L., Ye, J.: Optical interferometers with reduced sensitivity to thermal noise. Phys. Rev. Lett. 101(26), 260602 (2008). https://doi.org/10.1103/PhysRevLett.101.260602
DiMario, M.T., Becerra, F.E.: Channel-noise tracking for sub-shot-noise-limited receivers with neural networks. Phys. Rev. Res. 3(1), 013200 (2021). https://doi.org/10.1103/PhysRevResearch.3.013200
Lohani, S., Ryan, T.: Glasser: Coherent optical communications enhanced by machine intelligence. Mach. Learn. Sci. Technol. 1, 035006 (2020). https://doi.org/10.1088/2632-2153/ab9c3d
Bilkis, M., Rosati, M., Yepes, R.M., Calsamiglia, J.: Real-time calibration of coherent-state receivers: learning by trial and error. Phys. Rev. Res. 2(3), 033295 (2020). https://doi.org/10.1103/PhysRevResearch.2.033295
Acknowledgements
This research was funded by the Independent Innovation Science Fund of National University of Defense Technology (22-ZZCX-036), the National Natural Science Foundation of China (62101559), National key basic research program of China (2021-JCJQ-JJ-0510), Scientific research program of National University of Defense Technology (ZK22-09), the Innovative Key Projects Promotion in Information and Communication College (No. YJKT-RC-2113) and the National University of Defense Technology under Grant No. 19-QNCXJ.
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Chang Guo. and Tianyi Wu wrote the main manuscript text. Jungang Yang and Chen Dong directed the research. Kezheng Dang and Yang Ran improved the paper. All authors reviewed the manuscript.
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Guo, C., Wu, T., Dang, K. et al. Quantum-enhanced measurement scheme for quadrature phase-shift-keying coherent states under thermal noise. Quantum Inf Process 23, 231 (2024). https://doi.org/10.1007/s11128-024-04449-z
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DOI: https://doi.org/10.1007/s11128-024-04449-z