Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Practical continuous variable quantum secret sharing scheme based on non-ideal quantum state preparation

Wu Xiao-Dong Huang Duan

Citation:

Practical continuous variable quantum secret sharing scheme based on non-ideal quantum state preparation

Wu Xiao-Dong, Huang Duan
PDF
HTML
Get Citation
  • Continuous variable quantum secret sharing protocol can guarantee the unconditional security of secret key information based on the fundamental laws of physics. However, the state preparation operation may become non-ideal and imperfect in practical continuous variable quantum secret sharing scheme, which will introduce additional excess noise and affect the security of the scheme. Therefore, it is necessary to analyze it. We propose a practical continuous variable quantum secret sharing protocol based on imperfect state preparation. Specifically, in the proposed scheme, we assume that there are multiple users, and the imperfect state preparation performed by any user is equivalent to the corresponding untrusted third party using a phase insensitive amplifier to amplify the ideal modulator and laser owned by the user. The equivalent excess noise introduced by the imperfect state preparation can be calculated comprehensively and quantitatively through the gain of the corresponding phase insensitive amplifier. The results show that the continuous variable quantum secret sharing scheme is sensitive to the excess noise introduced by the imperfect state preparation operation, which will inevitably reduce its performance and security. Fortunately, the upper bound of the additional excess noise tolerance for the imperfect state preparation is achieved by using the specific gain formula of the phase insensitive amplifier, thus the security risks caused by the imperfect state preparation can be effectively solved. Due to considering the additional excess noise introduced by imperfect state preparation, tighter secret key rate curves can be obtained by the proposed scheme than those by the ideal continuous variable quantum secret sharing protocol. These results indicate that the proposed scheme can improve the practical security of continuous variable quantum secret sharing scheme, and provide a theoretical basis for its practical applications.
      Corresponding author: Huang Duan, duanhuang@csu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61972418, 61977062, 61801522) and the Scientific Research Initiation Fund of Fujian University of Technology, China (Grant No. GY-Z22042).
    [1]

    Liu H, Jiang C, Zhu H T, Zou M, Yu Z W, Hu X L, Xu H, Ma S, Han Z, Chen J P, Dai Y, Tang S B, Zhang W, Li H, You L, Wang Z, Hua Y, Hu H, Zhang H, Zhou F, Zhang Q, Wang X B, Chen T Y, Pan J W 2021 Phys. Rev. Lett. 126 250502Google Scholar

    [2]

    Xu F, Ma X, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002Google Scholar

    [3]

    Pirandola S, Andersen U L, Banchi L, Berta M, Bunandar D, Colbeck R, Englund D, Gehring T, Lupo C, Ottaviani C, Pereira J L, Razavi M, Shaari J S, Tomamichel M, Usenko V C, Vallone G, Villoresi P, Wallden P 2020 Adv. Opt. Photon. 12 1012Google Scholar

    [4]

    Wang S, Yin Z Q, He D Y, Chen W, Wang R Q, Ye P, Zhou Y, Fan-Yuan G J, Wang F X, Chen W, Zhu Y G, Morozov P V, Divochiy A V, Zhou Z, Guo G C, Han Z F 2022 Nat. Photon. 16 154Google Scholar

    [5]

    Yin J, Li Y H, Liao S K, Yang M, Cao Y, Zhang L, Ren J G, Cai W Q, Liu W Y, Li S L, Shu R, Huang Y M, Deng L, Li L, Zhang Q, Liu N L, Chen Y A, Lu C Y, Wang X B, Xu F H, Wang J Y, Peng C Z, Ekert A K, Pan J W 2020 Nature 582 501Google Scholar

    [6]

    Chen J P, Zhang C, Liu Y, Jiang C, Zhang W J, Han Z Y, Ma S Z, Hu X L, Li Y H, Liu H, Zhou F, Jiang H F, Chen T Y, Li H, You L X, Wang Z, Wang X B, Zhang Q, Pan J W 2021 Nat. Photon. 15 570Google Scholar

    [7]

    Wang S, He D Y, Yin Z Q, Lu F Y, Cui C H, Chen W, Zhou Z, Guo G C, Han Z F 2019 Phys. Rev. X 9 021046

    [8]

    Liu W Z, Zhang Y Z, Zhen Y Z, Li M H, Liu Y, Fan J , Xu F, Zhang Q, Pan J W 2022 Phys. Rev. Lett. 129 050502

    [9]

    吴晓东, 黄端, 黄鹏, 郭迎 2022 物理学报 71 240304Google Scholar

    Wu X D, Huang D, Huang P, Guo Y 2022 Acta Phys. Sin. 71 240304Google Scholar

    [10]

    Wu X D, Wang Y J, Zhong H, Liao Q, Guo Y 2019 Front. Phys. 14 41501Google Scholar

    [11]

    钟海, 叶炜, 吴晓东, 郭迎 2021 物理学报 70 020301Google Scholar

    Zhong H, Ye W, Wu X D, Guo Y 2021 Acta Phys. Sin. 70 020301Google Scholar

    [12]

    Grosshans F, Grangier P 2002 Phys. Rev. Lett. 88 057902Google Scholar

    [13]

    Huang D, Huang P, Lin D , Zeng G 2016 Sci. Rep. 6 19201

    [14]

    Zhang Y, Chen Z, Pirandola S, Wang X, Zhou C, Chu B, Zhao Y, Xu B, Yu S, Guo H 2020 Phys. Rev. Lett. 125 010502Google Scholar

    [15]

    Grosshans F, Assche G V, Wenger J, Brouri R, Cerf N J, Grangier P 2003 Nature (London) 421 238Google Scholar

    [16]

    Leverrier A 2015 Phys. Rev. Lett. 114 070501Google Scholar

    [17]

    Laudenbach F, Pacher C, Fung C H F, Poppe A, Peev M, Schrenk B, Hentschel M, Walther P, Hübel H 2018 Adv. Quantum Technol. 1 1800011Google Scholar

    [18]

    Leverrier A 2017 Phys. Rev. Lett. 118 200501Google Scholar

    [19]

    Chen Z, Zhang Y, Wang G, Li Z, Guo H 2018 Phys. Rev. A 98 012314Google Scholar

    [20]

    Qi B, Evans P G, Grice W P 2018 Phys. Rev. A 97 012317Google Scholar

    [21]

    Qi B, Gunther H, Evans P G, Williams B P, Camacho R M, Peters N A 2020 Phys. Rev. Appl. 13 054065Google Scholar

    [22]

    Huang P, Wang T, Chen R, Wang P, Zhou Y, Zeng G 2021 New J. Phys. 23 113028Google Scholar

    [23]

    Wu X, Wang Y, Guo Y, Zhong H, Huang D 2021 Phys. Rev. A 103 032604Google Scholar

    [24]

    Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1829Google Scholar

    [25]

    Kogias I, Xiang Y, He Q Y, Adesso G 2017 Phys. Rev. A 95 012315Google Scholar

    [26]

    Schmid C, Trojek P, Bourennane M, Kurtsiefer C, Zukowski M, Weinfurter H 2005 Phys. Rev. Lett. 95 230505Google Scholar

    [27]

    He G P 2007 Phys. Rev. Lett. 98 028901Google Scholar

    [28]

    Schmid C, Trojek P, Bourennane M, Kurtsiefer C, Zukowski M, Weinfurter H 2007 Phys. Rev. Lett. 98 028902Google Scholar

    [29]

    He G P, Wang Z D 2010 Quantum Inf. Comput. 10 28

    [30]

    Grice W P, Qi B 2019 Phys. Rev. A 100 022339Google Scholar

    [31]

    Wu X , Wang Y, Huang D 2020 Phys. Rev. A 101 022301Google Scholar

    [32]

    Liao Q, Liu H, Zhu L, Guo Y 2021 Phys. Rev. A 103 032410Google Scholar

    [33]

    Liu W, Wang X, Wang N, Du S, Li Y 2017 Phys. Rev. A 96 042312Google Scholar

    [34]

    Shen Y, Yang J, Guo H 2009 J. Phys. B: At. Mol. Opt. Phys. 42 235506Google Scholar

    [35]

    Usenko V C, Filip R 2010 Phys. Rev. A 81 022318Google Scholar

    [36]

    Jouguet P, Kunz J S, Diamanti E, Leverrier A 2012 Phys. Rev. A 86 032309Google Scholar

    [37]

    Fossier S, Diamanti E, Debuisschert T, Tualle-Brouri R, Grangier P 2009 J. Phys. B: At. Mol. Opt. Phys. 42 114014Google Scholar

    [38]

    Diamanti E, Leverrier A 2015 Entropy 17 6072Google Scholar

    [39]

    Lodewyck J, Bloch M, García-Patrón R, Fossier S, Karpov E, Diamanti E, Debuisschert T, Cerf N J, Tualle-Brouri R, McLaughlin S W, Grangier P 2007 Phys. Rev. A 76 042305Google Scholar

    [40]

    Huang P, He G Q, Zeng G H 2013 Int. J. Theor. Phys. 52 1572Google Scholar

    [41]

    Huang D, Huang P, Wang T, Li H, Zhou Y, Zeng G 2016 Phys. Rev. A 94 032305Google Scholar

    [42]

    Zhang H, Fang J, He G 2012 Phys. Rev. A 86 022338Google Scholar

    [43]

    Pirandola S, Laurenza R, Ottaviani C, Banchi L 2017 Nat. Commun. 8 15043Google Scholar

  • 图 1  基于非理想量子态制备的实际CV-QSS方案. AM为振幅调制器, PM为相位调制器, DHD为共扼零差探测, HABS为高度非对称分束器, ${Q_s}{\text{ (}}s = 1, {\text{ 2, }} \cdots {, }M)$表示第$s$个用户${U_s}$处的相位非敏感放大器

    Figure 1.  Practical CV-QSS scheme based on imperfect quantum state preparation. AM, amplitude modulator; PM, phase modulator; DHD, double homodyne detection; HABS, highly asymmetric beam splitter; ${Q_s}{\text{ (}}s = 1, {\text{ 2, }} \cdots {, }M)$, phase insensitive amplifier at the s-th user.

    图 2  基于非理想量子态制备的CV-QSS制备-测量方案图. QM为量子存储器, $T$表示非可信信道的透过率, ${\chi _{{\text{line}}}}$表示信道附加噪声

    Figure 2.  Schematic diagram of the prepare-and-measure (PM) model of the practical CV-QSS scheme based on imperfect quantum state preparation. QM, quantum memory; $T$, transmission efficiency; ${\chi _{{\text{line}}}}$, channel-added noise.

    图 3  基于非理想量子态制备的CV-QSS纠缠模型方案图

    Figure 3.  Schematic diagram of the entanglement-based (EB) model of the practical CV-QSS scheme based on imperfect quantum state preparation.

    图 4  所提出方案的密钥率与调制方差的关系 (a) 不同传输距离$L$; (b) 不同用户数量$M$

    Figure 4.  The relationship between the secret key rate of the proposed scheme and the modulation variance under: (a) Different transmission distance $L$; (b) different numbers of users $M$.

    图 5  所提出方案的密钥率与传输距离的关系 (a) $g = 1$; (b) $g = 1.001$; (c) $g = 1.002$; (d) $g = 1.003$

    Figure 5.  The relationship between the secret key rate of the proposed scheme and the transmission distance: (a) $g = 1$; (b) $g = $$ 1.001$; (c) $g = 1.002$; (d) $g = 1.003$.

    图 6  在不同传输距离$L$下, 所提出方案的密钥率与增益参数$g$的关系

    Figure 6.  The relationship between the secret key rate of the proposed scheme and the gain g under different transmission distances $L$.

  • [1]

    Liu H, Jiang C, Zhu H T, Zou M, Yu Z W, Hu X L, Xu H, Ma S, Han Z, Chen J P, Dai Y, Tang S B, Zhang W, Li H, You L, Wang Z, Hua Y, Hu H, Zhang H, Zhou F, Zhang Q, Wang X B, Chen T Y, Pan J W 2021 Phys. Rev. Lett. 126 250502Google Scholar

    [2]

    Xu F, Ma X, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002Google Scholar

    [3]

    Pirandola S, Andersen U L, Banchi L, Berta M, Bunandar D, Colbeck R, Englund D, Gehring T, Lupo C, Ottaviani C, Pereira J L, Razavi M, Shaari J S, Tomamichel M, Usenko V C, Vallone G, Villoresi P, Wallden P 2020 Adv. Opt. Photon. 12 1012Google Scholar

    [4]

    Wang S, Yin Z Q, He D Y, Chen W, Wang R Q, Ye P, Zhou Y, Fan-Yuan G J, Wang F X, Chen W, Zhu Y G, Morozov P V, Divochiy A V, Zhou Z, Guo G C, Han Z F 2022 Nat. Photon. 16 154Google Scholar

    [5]

    Yin J, Li Y H, Liao S K, Yang M, Cao Y, Zhang L, Ren J G, Cai W Q, Liu W Y, Li S L, Shu R, Huang Y M, Deng L, Li L, Zhang Q, Liu N L, Chen Y A, Lu C Y, Wang X B, Xu F H, Wang J Y, Peng C Z, Ekert A K, Pan J W 2020 Nature 582 501Google Scholar

    [6]

    Chen J P, Zhang C, Liu Y, Jiang C, Zhang W J, Han Z Y, Ma S Z, Hu X L, Li Y H, Liu H, Zhou F, Jiang H F, Chen T Y, Li H, You L X, Wang Z, Wang X B, Zhang Q, Pan J W 2021 Nat. Photon. 15 570Google Scholar

    [7]

    Wang S, He D Y, Yin Z Q, Lu F Y, Cui C H, Chen W, Zhou Z, Guo G C, Han Z F 2019 Phys. Rev. X 9 021046

    [8]

    Liu W Z, Zhang Y Z, Zhen Y Z, Li M H, Liu Y, Fan J , Xu F, Zhang Q, Pan J W 2022 Phys. Rev. Lett. 129 050502

    [9]

    吴晓东, 黄端, 黄鹏, 郭迎 2022 物理学报 71 240304Google Scholar

    Wu X D, Huang D, Huang P, Guo Y 2022 Acta Phys. Sin. 71 240304Google Scholar

    [10]

    Wu X D, Wang Y J, Zhong H, Liao Q, Guo Y 2019 Front. Phys. 14 41501Google Scholar

    [11]

    钟海, 叶炜, 吴晓东, 郭迎 2021 物理学报 70 020301Google Scholar

    Zhong H, Ye W, Wu X D, Guo Y 2021 Acta Phys. Sin. 70 020301Google Scholar

    [12]

    Grosshans F, Grangier P 2002 Phys. Rev. Lett. 88 057902Google Scholar

    [13]

    Huang D, Huang P, Lin D , Zeng G 2016 Sci. Rep. 6 19201

    [14]

    Zhang Y, Chen Z, Pirandola S, Wang X, Zhou C, Chu B, Zhao Y, Xu B, Yu S, Guo H 2020 Phys. Rev. Lett. 125 010502Google Scholar

    [15]

    Grosshans F, Assche G V, Wenger J, Brouri R, Cerf N J, Grangier P 2003 Nature (London) 421 238Google Scholar

    [16]

    Leverrier A 2015 Phys. Rev. Lett. 114 070501Google Scholar

    [17]

    Laudenbach F, Pacher C, Fung C H F, Poppe A, Peev M, Schrenk B, Hentschel M, Walther P, Hübel H 2018 Adv. Quantum Technol. 1 1800011Google Scholar

    [18]

    Leverrier A 2017 Phys. Rev. Lett. 118 200501Google Scholar

    [19]

    Chen Z, Zhang Y, Wang G, Li Z, Guo H 2018 Phys. Rev. A 98 012314Google Scholar

    [20]

    Qi B, Evans P G, Grice W P 2018 Phys. Rev. A 97 012317Google Scholar

    [21]

    Qi B, Gunther H, Evans P G, Williams B P, Camacho R M, Peters N A 2020 Phys. Rev. Appl. 13 054065Google Scholar

    [22]

    Huang P, Wang T, Chen R, Wang P, Zhou Y, Zeng G 2021 New J. Phys. 23 113028Google Scholar

    [23]

    Wu X, Wang Y, Guo Y, Zhong H, Huang D 2021 Phys. Rev. A 103 032604Google Scholar

    [24]

    Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1829Google Scholar

    [25]

    Kogias I, Xiang Y, He Q Y, Adesso G 2017 Phys. Rev. A 95 012315Google Scholar

    [26]

    Schmid C, Trojek P, Bourennane M, Kurtsiefer C, Zukowski M, Weinfurter H 2005 Phys. Rev. Lett. 95 230505Google Scholar

    [27]

    He G P 2007 Phys. Rev. Lett. 98 028901Google Scholar

    [28]

    Schmid C, Trojek P, Bourennane M, Kurtsiefer C, Zukowski M, Weinfurter H 2007 Phys. Rev. Lett. 98 028902Google Scholar

    [29]

    He G P, Wang Z D 2010 Quantum Inf. Comput. 10 28

    [30]

    Grice W P, Qi B 2019 Phys. Rev. A 100 022339Google Scholar

    [31]

    Wu X , Wang Y, Huang D 2020 Phys. Rev. A 101 022301Google Scholar

    [32]

    Liao Q, Liu H, Zhu L, Guo Y 2021 Phys. Rev. A 103 032410Google Scholar

    [33]

    Liu W, Wang X, Wang N, Du S, Li Y 2017 Phys. Rev. A 96 042312Google Scholar

    [34]

    Shen Y, Yang J, Guo H 2009 J. Phys. B: At. Mol. Opt. Phys. 42 235506Google Scholar

    [35]

    Usenko V C, Filip R 2010 Phys. Rev. A 81 022318Google Scholar

    [36]

    Jouguet P, Kunz J S, Diamanti E, Leverrier A 2012 Phys. Rev. A 86 032309Google Scholar

    [37]

    Fossier S, Diamanti E, Debuisschert T, Tualle-Brouri R, Grangier P 2009 J. Phys. B: At. Mol. Opt. Phys. 42 114014Google Scholar

    [38]

    Diamanti E, Leverrier A 2015 Entropy 17 6072Google Scholar

    [39]

    Lodewyck J, Bloch M, García-Patrón R, Fossier S, Karpov E, Diamanti E, Debuisschert T, Cerf N J, Tualle-Brouri R, McLaughlin S W, Grangier P 2007 Phys. Rev. A 76 042305Google Scholar

    [40]

    Huang P, He G Q, Zeng G H 2013 Int. J. Theor. Phys. 52 1572Google Scholar

    [41]

    Huang D, Huang P, Wang T, Li H, Zhou Y, Zeng G 2016 Phys. Rev. A 94 032305Google Scholar

    [42]

    Zhang H, Fang J, He G 2012 Phys. Rev. A 86 022338Google Scholar

    [43]

    Pirandola S, Laurenza R, Ottaviani C, Banchi L 2017 Nat. Commun. 8 15043Google Scholar

  • [1] He Ying, Wang TianYi, Li YingYing. Composable security analysis of linear optics cloning machine enhanced discretized polar modulation continuous-variable quantum key distribution. Acta Physica Sinica, 2024, 73(23): . doi: 10.7498/aps.20241094
    [2] He Ying, Wang Tian-Yi, Li Ying-Ying. Composable security analysis of linear optics cloning machine improved discretized polar modulation continuous-variable quantum key distribution. Acta Physica Sinica, 2024, 73(23): 230303. doi: 10.7498/aps.73.20241094
    [3] Wu Xiao-Dong, Huang Duan, Huang Peng, Guo Ying. Discrete modulation continuous-variable measurement-device-independent quantum key distribution scheme based on realistic detector compensation. Acta Physica Sinica, 2022, 71(24): 240304. doi: 10.7498/aps.71.20221072
    [4] Wang Mei-Hong, Hao Shu-Hong, Qin Zhong-Zhong, Su Xiao-Long. Research advances in continuous-variable quantum computation and quantum error correction. Acta Physica Sinica, 2022, 71(16): 160305. doi: 10.7498/aps.71.20220635
    [5] Wen Zhen-Nan, Yi You-Gen, Xu Xiao-Wen, Guo Ying. Continuous variable quantum teleportation with noiseless linear amplifier. Acta Physica Sinica, 2022, 71(13): 130307. doi: 10.7498/aps.71.20212341
    [6] Zhong Hai, Ye Wei, Wu Xiao-Dong, Guo Ying. Optical preamplifier based simultaneous quantum key distribution and classical communication scheme. Acta Physica Sinica, 2021, 70(2): 020301. doi: 10.7498/aps.70.20200855
    [7] Zhai Shu-Qin, Kang Xiao-Lan, Liu Kui. Quantum steering based on cascaded four-wave mixing processes. Acta Physica Sinica, 2021, 70(16): 160301. doi: 10.7498/aps.70.20201981
    [8] Mao Yi-Yu, Wang Yi-Jun, Guo Ying, Mao Yu-Hao, Huang Wen-Ti. Continuous-variable quantum key distribution based on peak-compensation. Acta Physica Sinica, 2021, 70(11): 110302. doi: 10.7498/aps.70.20202073
    [9] Ye Wei, Guo Ying, Xia Ying, Zhong Hai, Zhang Huan, Ding Jian-Zhi, Hu Li-Yun. Discrete modulation continuous-variable quantum key distribution based on quantum catalysis. Acta Physica Sinica, 2020, 69(6): 060301. doi: 10.7498/aps.69.20191689
    [10] Luo Jun-Wen, Wu De-Wei, Li Xiang, Zhu Hao-Nan, Wei Tian-Li. Continuous variable polarization entanglement in microwave domain. Acta Physica Sinica, 2019, 68(6): 064204. doi: 10.7498/aps.68.20181911
    [11] Liang Jian-Wu, Cheng Zi, Shi Jin-Jing, Guo Ying. Quantum secret sharing with quantum graph states. Acta Physica Sinica, 2016, 65(16): 160301. doi: 10.7498/aps.65.160301
    [12] Wei Ke-Jin, Ma Hai-Qiang, Wang Long. A quantum secret sharing scheme based on two polarization beam splitters. Acta Physica Sinica, 2013, 62(10): 104205. doi: 10.7498/aps.62.104205
    [13] Xu Bing-Jie, Tang Chun-Ming, Chen Hui, Zhang Wen-Zheng, Zhu Fu-Chen. Improving the maximum transmission distance of coutinuous variable no-switching QKD protocol. Acta Physica Sinica, 2013, 62(7): 070301. doi: 10.7498/aps.62.070301
    [14] Yan Zhi-Hui, Jia Xiao-Jun, Xie Chang-De, Peng Kun-Chi. Continuous-variable three-color tripartite entangled state generated by a non-degenerate optical parameter oscillator. Acta Physica Sinica, 2012, 61(1): 014206. doi: 10.7498/aps.61.014206
    [15] Song Han-Chong, Gong Li-Hua, Zhou Nan-Run. Continuous-variable quantum deterministic key distribution protocol based on quantum teleportation. Acta Physica Sinica, 2012, 61(15): 154206. doi: 10.7498/aps.61.154206
    [16] Zhu Chang-Hua, Chen Nan, Pei Chang-Xing, Quan Dong-Xiao, Yi Yun-Hui. Adaptive continuous variable quantum key distribution based on channel estimation. Acta Physica Sinica, 2009, 58(4): 2184-2188. doi: 10.7498/aps.58.2184
    [17] Sun Ying, Du Jian-Zhong, Qin Su-Juan, Wen Qiao-Yan, Zhu Fu-Chen. Quantum secret sharing with bidirectional authentication. Acta Physica Sinica, 2008, 57(8): 4689-4694. doi: 10.7498/aps.57.4689
    [18] Entanglement property of two-mode cavity field in a nondegenerate four-wave mixing system. Acta Physica Sinica, 2007, 56(12): 6970-6975. doi: 10.7498/aps.56.6970
    [19] Chen Jin-Jian, Han Zheng-Fu, Zhao Yi-Bo, Gui You-Zhen, Guo Guang-Can. The effect of balanced homodyne detection on continuous variable quantum key distribution. Acta Physica Sinica, 2007, 56(1): 5-9. doi: 10.7498/aps.56.5
    [20] Yang Yu-Guang, Wen Qiao-Yan, Zhu Fu-Chen. Single N-dimensional quNit quantum secret sharing. Acta Physica Sinica, 2006, 55(7): 3255-3258. doi: 10.7498/aps.55.3255
Metrics
  • Abstract views:  2123
  • PDF Downloads:  65
  • Cited By: 0
Publishing process
  • Received Date:  03 February 2023
  • Accepted Date:  28 October 2023
  • Available Online:  16 November 2023
  • Published Online:  20 January 2024

/

返回文章
返回