-
In a practical continuous-variable quantum secret sharing system, the local oscillator transmitted via an insecure channel may be subject to security threats due to various targeted attacks. To address this problem, this paper proposes a continuous-variable quantum secret sharing scheme with local local oscillator, in which the local oscillator is generated locally at the trusted end without being sent by each user, thus completely plugging the relevant security loopholes. The scheme consists of three stages: preparation, where users generate Gaussian-modulated coherent states and reference signals; measurement, where the dealer performs heterodyne detection using the local local oscillator and reference phases; and post-processing, involving parameter estimation, phase compensation, and secure key extraction. On this basis, Kalman filter is utilized to estimate the minimum mean square error for each reference phase separately, reducing the phase drift estimation error and suppressing the phase measurement noise. Phase compensation methods for scalar Kalman filter and vector Kalman filter are developed respectively, where scalar KF requires additional block averaging for slow phase drift, while vector KF simultaneously models fast and slow drifts, enabling one-step compensation with minimized estimation errors. The excess noise of the filtered system including modulation noise, phase noise, photon leakage noise, and ADC quantization noise is modeled, with KF reducing phase measurement noise via dynamic gain optimization. Security bound against eavesdroppers and dishonest users is derived. Numerical simulations under practical parameters demonstrate significant improvements: vector KF achieves a maximum transmission distance of 82.6 km (vs. 67.3 km for block averaging) and supports 33 users (vs. 22), with excess noise reduced by 40% at 60 km. The scheme’s robustness is further validated under varying reference signal amplitudes, showing stable performance even with lower, minimizing interference with quantum signals. These results highlight the proposed scheme has significant advantages in terms of maximum transmission distance and maximum number of supported users, and has the potential to build adaptive KF algorithms for dynamic user scenarios and quantum machine learning integration.
-
Keywords:
- quantum secret sharing /
- continuous variable /
- local local oscillator /
- Kalman filter
-
[1] Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1829
[2] Karlsson A, Koashi M, Imoto N 1999 Phys. Rev. A 59 162
[3] Tyc T, Sanders B C 2002 Phys. Rev. A 65 042310
[4] Lance A M, Symul T, Bowen W P, Tyc T, Sanders B C, Lam P K 2003 New J. Phys. 5 4
[5] Liao Q, Xiao G, Xu C G, Xu Y, Guo Y 2020 Phys. Rev. A 102 032604
[6] Kogias I, Xiang Y, He Q, Adesso G 2017 Phys. Rev. A 95 012315
[7] Grice W P, Qi B 2019 Phys. Rev. A 100 022339
[8] Wang Y, Jia B, Mao Y, Wu X, Guo Y 2020 Appl. Sci. 10 2411
[9] Liao Q, Liu H, Zhu L, Guo Y 2021 Phys. Rev. A 103 032410
[10] Liao Q, Liu X, Ou B, Fu X 2023 IEEE Trans. Commun. 71 6051-6060
[11] Liao Q, Wang Z, Liu H, Mao Y, Fu X 2022 Phys. Rev. A 106 022607
[12] Ma X C, Sun S H, Jiang M S, Liang L M 2013 Phys. Rev. A-Atom. Mol. Opt. Phy. 87 052309
[13] Jouguet P, Kunz-Jacques S, Diamanti E 2013 Phys. Rev. A-Atom. Mol. Opt. Phy. 87 062313
[14] Ma X C, Sun S H, Jiang M S, Liang L M 2013 Phys. Rev. A-Atom. Mol. Opt. Phy. 88 022339
[15] Zhao Y, Zhang Y, Huang Y, Xu B, Yu S, Guo H 2018 J. Phys. B-At. Mol. Opt. Phy. 52 015501
[16] Zheng Y, Huang P, Peng J Y, Zeng G H 2019 Information and Communications Technology and Policy 45 43 (in Chinese) [郑异, 黄鹏, 彭进业, 曾贵华 2019 信息通信技术与政策 45 43]
[17] Liao Q, Huang L, Fei Z Y, Fu X Q 2025 Adv. Quantum Technol. 2400505
[18] Kunz-Jacques S, Jouguet P 2015 Phys. Rev. A 91 022307
[19] Mao Y, Huang W, Zhong H, Wang Y, Qin H, Guo Y, Huang D 2020 New J. Phys. 22 083073
[20] Liao Q, Liu H, Gong Y, Wang Z, Peng Q, Guo Y 2022 Opt. Express 30 3876-3892
[21] Qi B, Lougovski P, Pooser R, Grice W, Bobrek M 2015 Phys. Rev. X 5 041009
[22] Wang T, Huang P, Zhou Y, Liu W, Ma H, Wang S, Zeng G 2018 Opt. Express 26 2794-2806
[23] Wang H, Li Y, Pi Y D, Pan Y, Shao Y, Ma L, Zhang Y C, Yang J, Zhang T, Huang W, Xu B J 2022 Commun. Phys. 5 162
[24] Marie A, Alléaume R 2017 Phys. Rev. A 95 012316
[25] Wang H, Pi Y D, Huang W, Li Y, Shao Y, Yang J, Liu J L, Zhang C L, Zhang Y C, Xu B J 2020 Opt. Express 28 32882-32893
[26] Zhang Y, Bian Y, Li Z, Yu S, Guo H 2024 Appl. Phys. Rev. 11
[27] Huang B, Ma T T, Huang Y M, Peng Z M 2021 Laser Optoelectron. Prog. 58 1127001 (in Chinese) [黄彪, 麻甜甜, 黄永梅, 彭真明 2021 激光与光电子学进展 58 1127001]
[28] Roy S, Petersen I R, Huntington E H 2015 New J. Phys. 17 063020
[29] Liu X C, Wen J X, Li S B, Li H G, Sun S L 2023 Chin. J. Lasers 50 1412002-1412002 (in Chinese) [刘旭超, 温佳旭, 李少波, 李华贵, 孙时伦 2023 中国激光 50 1412002-1412002]
[30] Shen T, Wang X, Chen Z, Tian H, Yu S, Guo H 2023 IEEE Photonics J. 15 1-9
[31] Ren S, Kumar R, Wonfor A, Tang X, Penty R, White I 2019 JOSA B 36 B7-B15
[32] Huang B, Huang Y M, Peng Z M 2019 Acta Opt. Sin. 39 1127001 (in Chinese) [黄彪, 黄永梅, 彭真明 2019 光学学报 39 1127001]
[33] Roy S, Rehman O U, Petersen I R, Huntington E H 2014 European Control Con-ference p896-901
[34] Wang T, Huang P, Wang S, Zeng G 2019 Opt. Express 27 26689-26700
[35] Hajomer A A, Derkach I, Jain N, Chin H M, Andersen U L, Gehring T 2024 Sci. Adv. 10 eadi9474
[36] Su Y, Guo Y, Huang D 2019 Phys. Lett. A 383 2394-2399
[37] Huang B, Huang Y, Peng Z 2020 Opt. Express 28 28727-28739
[38] Zhong H, Ye W, Zuo Z, Huang D, Guo Y 2022 Opt. Express 30 5981-6002
[39] Diamanti E, Leverrier A 2015 Entropy 17 6072-6092
[40] Inoue T, Namiki S 2014 Opt. Express 22 15376-15387
[41] Huang B, Huang Y, Peng Z 2019 Opt. Express 27 20621-20631
[42] Shao Y, Pan Y, Wang H, Pi Y D, Li Y, Ma L, Zhang Y C, Huang W, Xu B J 2022 Entropy 24 992
[43] Shao Y, Wang H, Pi Y D, Huang W, Li Y, Liu J L, Yang J, Zhang Y C, Xu B J 2021 Phys. Rev. A 104 032608
[44] Kish S P, Villaseñor E, Malaney R, Mudge K A, Grant K J 2021 IEEE Interna-tional Conference on Communications p1-6
[45] Shao Y, Li Y, Wang H, Pan Y, Pi Y D, Zhang Y C, Huang W, Xu B J 2022 Phys. Rev. A 105 032601
[46] Wang T, Huang P, Zhou Y, Liu W, Zeng G 2018 Phys. Rev. A 97 012310
[47] Huang P, Lin D K, Huang D, Zeng, G H 2015 Int. J. Theor. Phys. 54 2613-2622
[48] Jouguet P, Kunz-Jacques S, Diamanti E, Leverrier A 2012 Phys. Rev. A-Atom. Mol. Opt. Phy. 86 032309
[49] Huang D, Huang P, Lin D, Zeng G 2016 Sci. Rep. 6 19201
[50] Chin H M, Jain N, Zibar D, Andersen U L, Gehring T 2021 Npj Quantum Inf. 7 20
[51] Sun Y H, Chen Z Y, Wang X Y, Yu S, Guo H 2025 Phys. Rev. Appl. 23(1) 014056
[52] Oruganti A N, Derkach I, Filip R, Usenko V C 2025 Quantum Sci. Technol. 10 025023
[53] Liu Y M, Jiang X Q, Dai J S, Hai H, Huang P 2025 Quantum Sci. Technol. 10 025043
[54] Liao Q, Fei Z Y, Huang L, Fu X Q 2025 Commun. Phys. 8(1) 138
[55] Ren S, Yang S, Wonfor A, White I, Penty R 2021 Sci. Rep. 11 9454
[56] Soh D B, Brif C, Coles P J, Lütkenhaus N, Camacho R M, Urayama J, Sarovar M 2015 Phys. Rev. X 5 041010
[57] Lodewyck J, Bloch M, García-Patrón R, Fossier S, Karpov E, Diamanti E, Debuisschert T, Debuisschert T, Cerf N J, Tualle-Brouri R, McLaughlin S W, Grangier P 2007 Phys. Rev. A-Atom. Mol. Opt. Phy. 76 042305
[58] Rui X, He H W, Sun F C, Zhao K 2013 IEEE Trans. Veh. Technol. 62(1) 108-117
[59] Liao Q, Fei Z Y, Liu J Y, Huang A Q, Huang L, Wang Y J 2025 Chaos Soliton. Fract. 196 116331
Metrics
- Abstract views: 78
- PDF Downloads: 1
- Cited By: 0
下载:
