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首先介绍了单次发送单光子的量子安全直接通信方案的具体步骤. 基于该方案的基本步骤, 逐步扩展到分两次和分四次发送单光子序列的量子安全直接通信方案, 重点介绍各方案对应的编码规则. 分析上述方案的效率可以看出, 发送次数的增加可以增加单光子的分类, 大大提高每个单光子的编码容量和整个通信中量子态的传输效率. 最后提出有通用性的分n (n为2的整数次幂)次发送单光子来进行量子安全直接通信的方案及其编码规则, 经过安全性分析证明方案安全可行. 通过效率分析, 该方案比现有方案的通信效率更高, 而且该方案的实施只用到单光子, 不涉及量子纠缠, 实现难度更小.In this work, we first introduce the specific steps of a quantum-secure direct communication scheme that sends a single photon at a time. Based on the basic steps of the scheme, it is gradually extended to a quantum secure direct communication scheme that transmits single-photon sequences twice and four times, with emphasis on the coding rules corresponding to each scheme. The purpose is that through the above scheme, it can be intuitively seen in the subsequent efficiency analysis that with the increase of the number of transmissions, the classification of single photons can be increased, and the encoding capacity of each single photon and the transmission efficiency of quantum states in the entire communication can be greatly improved. Finally, a universal scheme and coding rules for quantum secure direct communication by sending single photons in an integer power of 2 are proposed, and after security analysis the scheme proves to be safe and feasible. Through the efficiency analysis, the communication efficiency of this scheme is higher than that of the existing scheme, and the implementation of this scheme only uses a single photon, does not involve with quantum entanglement, and this scheme has more application values.
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Keywords:
- single photon /
- multiple sending /
- encoding rules /
- efficiency analysis
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Xin L 2019 M. S. Thesis (Lanzhou: Lanzhou University)
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Wang Z Y 2019 M. S. Thesis (Shenyang: Shenyang Gongye University)
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Zhou X T, Jiang Y H, Guo C F, Zhao N, Liu B 2021 Chin. J. Quantum Electron. https://kns.cnki.net/kcms/detail/34.1163.TN.20210927.2021.002.html (in Chinese)
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表 1 编码规则一
Table 1. Coding Rule 1.
信息序列 量子态 信息序列 量子态 00 $ \left| 0 \right\rangle $ 10 $ \left| + \right\rangle $ 11 $ \left| 1 \right\rangle $ 01 $ \left| - \right\rangle $ 
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表 2 编码规则二
Table 2. Coding Rule 2.
信息序列 量子态 信息序列 量子态 000 $ \left| {{0_1}} \right\rangle $ 001 $ \left| {{0_2}} \right\rangle $ 111 $ \left| {{1_1}} \right\rangle $ 110 $ \left| {{1_2}} \right\rangle $ 011 $ \left| {{ + _1}} \right\rangle $ 010 $ \left| {{ + _2}} \right\rangle $ 100 $ \left| {{ - _1}} \right\rangle $ 101 $ \left| {{ - _2}} \right\rangle $
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表 3 编码规则三
Table 3. Coding Rule 3.
信息序列 量子态 信息序列 量子态 0000 $ \left| {{0_1}} \right\rangle $ 1000 $ \left| {{0_3}} \right\rangle $ 1111 $ \left| {{1_1}} \right\rangle $ 0111 $ \left| {{1_3}} \right\rangle $ 0001 $ \left| {{ + _1}} \right\rangle $ 0011 $ \left| {{ + _3}} \right\rangle $ 1110 $ \left| {{ - _1}} \right\rangle $ 1100 $ \left| {{ - _3}} \right\rangle $ 0010 $ \left| {{0_2}} \right\rangle $ 0101 $ \left| {{0_4}} \right\rangle $ 1101 $ \left| {{1_2}} \right\rangle $ 1010 $ \left| {{1_4}} \right\rangle $ 0100 $ \left| {{ + _2}} \right\rangle $ 1001 $ \left| {{ + _4}} \right\rangle $ 1011 $ \left| {{ - _2}} \right\rangle $ 0110 $ \left| {{ - _4}} \right\rangle $
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表 4 编码规则四
Table 4. Coding Rule 4.
信息序列 量子态 $ \cdots $ 信息序列 量子态 $ \overbrace {0 \cdots 0}^{{{\log }_2}\left( {4 n} \right)} $ $ \left| {{0_1}} \right\rangle $ $ \cdots $ $ \overbrace {0 \cdots 10}^{{{\log }_2}\left( {4 n} \right)} $ $ \left| {{0_n}} \right\rangle $ $ \overbrace {1 \cdots 1}^{{{\log }_2}\left( {4 n} \right)} $ $ \left| {{1_1}} \right\rangle $ $ \cdots $ $ \overbrace {1 \cdots 01}^{{{\log }_2}\left( {4 n} \right)} $ $ \left| {{1_n}} \right\rangle $ $ \overbrace {0 \cdots 1}^{{{\log }_2}\left( {4 n} \right)} $ $ \left| {{ + _1}} \right\rangle $ $ \cdots $ $ \overbrace {0 \cdots 11}^{{{\log }_2}\left( {4 n} \right)} $ $ \left| {{ + _n}} \right\rangle $ $ \overbrace {1 \cdots 0}^{{{\log }_2}\left( {4 n} \right)} $ $ \left| {{ - _1}} \right\rangle $ $ \cdots $ $ \overbrace {1 \cdots 00}^{{{\log }_2}\left( {4 n} \right)} $ $ \left| {{ - _n}} \right\rangle $
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表 5 参数对比
Table 5. Parameter comparison.
QSDC通信协议 传输
效率量子比特率 编码容量 邓富国Two-Step [11] 1 1 1 qubit: 2 bit 权东晓基于单光子单向[12] 0.5 1 1 qubit: 1 bit 曹正文基于单光子与Bell态结合[13] 2 1 1 qubit: 3 bit 基于单光子与GHZ态结合[16] 2 1 1 qubit: 4 bit 基于单光子与n粒子GHZ态结合[17] 2 1 1 qubit: (1+n)bit 王剑基于纠缠交换[18] 1 1 1 qubit: 2 bit 单次发送单光子 2 1 1 qubit: 2 bit 分两次发送单光子 3 1 1 qubit: 3 bit 分4次发送单光子 4 1 1 qubit: 4 bit 分n(n是2的整数次幂)次
发送单光子$ {\text{lo}}{{\text{g}}_2}\left( {4 n} \right) $ 1 1 qubit:
$ {\text{lo}}{{\text{g}}_2}\left( {4 n} \right) $bit
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[1] 欣龙 2019 硕士学位论文 (兰州: 兰州大学)
Xin L 2019 M. S. Thesis (Lanzhou: Lanzhou University)
[2] Bennett C H, Brassard G 1984 Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing (New York: IEEE Press) p175
[3] Ekert A K 1991 Phys. Rev. Lett. 67 661
Google Scholar
[4] 王争艳 2019 硕士学位论文(沈阳: 沈阳工业大学)
Wang Z Y 2019 M. S. Thesis (Shenyang: Shenyang Gongye University)
[5] Sheng Y B, Zhou L, Long G L 2022 Science Bulletin. 67 367
Google Scholar
[6] Long G L, Liu X S 2002 Phys. Rev. A 65 032302
Google Scholar
[7] 余松, 柏明强, 唐茜, 莫智文 2021 量子电子学报 38 57
Yu S, Bo M Q,Tang Q, Mo Z W 2021 Chin. J. Quantum Electron 38 57
[8] Liu Z H, Chen H W 2013 Chin. Phys. Lett. 30 079901
Google Scholar
[9] Liu Z H, Chen H W, Liu W J 2016 Chin. Phys. Lett. 33 070305
Google Scholar
[10] Deng F G, Long G L, Liu X S 2003 Phys. Rev. A 68 042317
Google Scholar
[11] Deng F G, Long G L 2004 Phys. Rev. A 69 052319
Google Scholar
[12] 权东晓, 裴昌辛, 刘丹, 赵楠 2010 物理学报 59 2493
Google Scholar
Quan D X, Pei C X, Liu D, Zhao N 2010 Acta Phys. Sin. 59 2493
Google Scholar
[13] 曹正文, 赵光, 张爽浩, 冯晓毅, 彭进业 2016 物理学报 65 230301
Google Scholar
Cao Z W, Zhao G, Zhang S H, Feng X Y, Peng J Y 2016 Acta Phys. Sin. 65 230301
Google Scholar
[14] 刘志昊, 陈汉武 2017 物理学报 66 130304
Google Scholar
Liu Z H, Chen H W 2017 Acta Phys. Sin. 66 130304
Google Scholar
[15] 赵宁, 江英华, 周贤韬, 郭晨飞, 刘彪 2021 网络安全技术与应用 08 30
Google Scholar
Zhao N, Jiang Y H, Zhou X T, Guo C F, Liu B 2021 Network Security Technology 08 30
Google Scholar
[16] 周贤韬, 江英华, 郭晨飞, 赵宁, 刘彪 2021 量子电子学报 https://kns.cnki.net/kcms/detail/34.1163.TN.20210927.2021.002.html
Zhou X T, Jiang Y H, Guo C F, Zhao N, Liu B 2021 Chin. J. Quantum Electron. https://kns.cnki.net/kcms/detail/34.1163.TN.20210927.2021.002.html (in Chinese)
[17] 周贤韬, 江英华 2022 激光技术 46 79
Google Scholar
Zhou X T, Jiang Y H 2022 Laser Technology 46 79
Google Scholar
[18] 王剑, 张盛, 张守林, 张权 2009 国防科技大学学报 31 51
Google Scholar
Wang J, Zhang S, Zhang S L, Zhang Q 2009 J. Nat. Univ. Defense 31 51
Google Scholar
[19] 李雪杨, 昌燕, 张仕斌, 代金鞘, 郑涛 2020 计算机应用与软件 37 292
Google Scholar
Li X Y, Chang Y, Zhang S B, Dai J Q, Zheng T 2020 Computer Applications and Software 37 292
Google Scholar
[20] 危语嫣, 高子凯, 王思颖, 朱雅静, 李涛 2022 物理学报 71 050302
Google Scholar
Wei Y Y, Gao Z K, Wang S Y, Zhu Y J, Li T 2022 Acta. Phy. Sin. 71 050302
Google Scholar
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