Bi-directional semi-quantum secure direct communication protocol based on high-dimensional single-particle states

Gong Li-Hua; Chen Zhen-Yong; Xu Liang-Chao; Zhou Nan-Run

doi:10.7498/aps.71.20211702

Abstract

Semi-quantum secure direct communication allows the quantum party and the classical party to transmit secure messages directly, but does not need sharing a secret key in advance. To increase the information transmission efficiency and practicability of semi-quantum secure direct communication, a bidirectional semi-quantum secure direct communication protocol with high-dimensional single-particle states is designed. The proposed protocol involves quantum party Alice and classical party Bob. Each participant can receive a secret message while sending a secret message. Unlike most of existing quantum secure direct communication protocols, it is not necessary for the classical party Bob in the proposed protocol to possess the capability of measuring quantum states, which greatly enhances the feasibility of the protocol. The protocol allows the classical party Bob to implement the unitary operations on particles and reorder the quantum sequence. Furthermore, the quantum party Alice and the classical party Bob can verify the correctness of the received secret message with the Hash function. Security analysis indicates that without being discovered by the legitimate participants, Eve cannot obtain the secret message with common attack, such as intercept-resend attack, measure-resend attack, tampering attack and entanglement-measure attack. Compared with the typical semi-quantum secure direct communication protocols, the proposed protocol has a high qubit efficiency of about 28.6%. In addition, the transmission efficiency of secret message is greatly enhanced, since the proposed protocol utilizes the high-dimensional single-particle states as the carrier of secret message.

Keywords:

semi-quantum secure direct communication /
high-dimensional single-particle state /
bi-directional communication /
security analysis

Authors and contacts

Department of Electronics Information Engineering, Nanchang University, Nanchang 330031, China

Corresponding author: Zhou Nan-Run, znr21@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61871205).

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References

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[2]	Li X H, Ghose S 2015 Phys. Rev. A 91 012320 Google Scholar
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[13]	Wang Q Q, Zheng Y, Zhai C H, Li X D, Gong Q H, Wang J W 2021 J. Semicond. 42 091901 Google Scholar
[14]	Long G L, Liu X S 2002 Phys. Rev. A 65 032302 Google Scholar
[15]	Boström K, Felbinger T 2002 Phys. Rev. Lett. 89 187902 Google Scholar
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[17]	Deng F G, Long G L 2004 Phys. Rev. A 69 052319 Google Scholar
[18]	Wang C, Deng F G, Li Y S, Liu X S, Long G L 2005 Phys. Rev. A 71 044305 Google Scholar
[19]	Shi J, Gong Y X, Xu P, Zhu S N, Zhan Y B 2011 Commun. Theor. Phys. 56 831 Google Scholar
[20]	郑晓毅龙银香 2017 66 180303 Google Scholar Zheng X Y, Long Y X 2017 Acta Phys. Sin. 66 180303 Google Scholar
[21]	Chen S S, Zhou L, Zhong W, Sheng Y B 2018 Sci. Chin. -Phys. Mech. Astron. 61 90312 Google Scholar
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[34]	Zhou N R, Xu Q D, Du N S, Gong L H 2021 Quantum Inf. Process. 20 124 Google Scholar
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[37]	Gu J, Lin P H, Hwang T 2018 Quantum Inf. Process. 17 182 Google Scholar
[38]	Zhang M H, Li H F, Xia Z Q, Feng X Y, Peng J Y 2017 Quantum Inf. Process. 16 117 Google Scholar
[39]	Xie C, Li L Z, Situ H Z, He J H 2018 Int. J. Theor. Phys. 57 1881 Google Scholar
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[43]	Wen X J, Zhao X Q, Gong L H, Zhou N R 2019 Laser Phys. Lett. 16 075206 Google Scholar

Cited By

图 1 窃听检测概率

Figure 1. Eavesdropping detection probability.

DownLoad: Full-Size Img PowerPoint

图 2 单粒子传输秘密信息-维数

Figure 2. Single particle transport secret information - dimension.

DownLoad: Full-Size Img PowerPoint

表 1 操作后粒子的分类

Table 1. Classification of the particles after operation.

原始状态所属基	Bob的操作	标记为
$\overline Z $	CTRL	$\overline Z - {\text{CTRL}}$
$\overline Z $	${U_m}$	$\overline Z - U$
$\overline X $	CTRL	$\overline X - {\text{CTRL}}$
$\overline X $	${U_m}$	$\overline X - U$

DownLoad: CSV

表 2 Alice的窃听检测策略

Table 2. Eavesdropping detection strategy for Alice.

原始状态	Bob的操作	Alice的操作	预期结果
$\left\| k \right\rangle $	CTRL	$\overline Z $基测量	$\left\| k \right\rangle $
$\left\| k \right\rangle $	${U_m}$	$\overline Z $基测量	$\left\| {k \oplus m} \right\rangle $
$F\left\| k \right\rangle $	CTRL	$\overline X $基测量	$F\left\| k \right\rangle $
$F\left\| k \right\rangle $	${U_m}$	$\overline X $基测量	$F\left\| k \right\rangle $

DownLoad: CSV

表 3 Eve的截获重发攻击

Table 3. Intercept-resend attack by Eve.

Alice发送的粒子	Bob的操作	Eve的操作	Alice的操作	窃听是否会被发现
$\overline Z $	CTRL	CTRL	用$\overline Z $基测量	否
$\overline Z $	CTRL	${U_m}$	用$\overline Z $基测量	是
$\overline Z $	${U_m}$	CTRL	用$\overline Z $基测量	$\dfrac{ {d - 1} }{ {2 d} }$的概率被发现
$\overline Z $	${U_m}$	${U_m}$	用$\overline Z $基测量	$\dfrac{ {d - 1} }{ {2 d} }$的概率被发现
$\overline X $	CTRL	CTRL	用$\overline X $基测量	否
$\overline X $	CTRL	${U_m}$	用$\overline X $基测量	否
$\overline X $	${U_m}$	CTRL	用$\overline X $基测量	否
$\overline X $	${U_m}$	${U_m}$	用$\overline X $基测量	否

DownLoad: CSV

表 4 Eve的测量重发攻击

Table 4. Measurement-resend attack by Eve.

Alice发送的粒子	Eve的测量基	Bob得到的粒子	Bob的操作	Alice的操作	窃听是否被发现
$\overline Z $	$\overline Z $	$\overline Z $	CTRL	$\overline Z $基测量	否
$\overline Z $	$\overline Z $	$\overline Z $	${U_m}$	$\overline Z $基测量	否
$\overline Z $	$\overline X $	$\overline X $	CTRL	$\overline Z $基测量	$\dfrac{ {d - 1} }{d}$概率被发现
$\overline Z $	$\overline X $	$\overline X $	${U_m}$	$\overline Z $基测量	$\dfrac{ {d - 1} }{ {2 d} }$概率被发现
$\overline X $	$\overline Z $	$\overline Z $	CTRL	$\overline X $基测量	$\dfrac{ {d - 1} }{d}$概率被发现
$\overline X $	$\overline Z $	$\overline Z $	${U_m}$	$\overline X $基测量	$\dfrac{ {d - 1} }{d}$概率被发现
$\overline X $	$\overline X $	$\overline X $	CTRL	$\overline X $基测量	否
$\overline X $	$\overline X $	$\overline X $	${U_m}$	$\overline X $基测量	否

DownLoad: CSV

表 5 本协议与现有经典SQSDC协议的比较

Table 5. Comparison of the proposed protocol with existing classical SQSDC protocols.

协议	文献[36]	文献[38]	协议一[40]	协议二[40]	本文协议
量子载体	二维单粒子态	二维Bell态	二维Bell态	二维Bell态	$d$维单粒子态
通信模式	单向	单向	单向	单向	双向
经典方是否需要测量能力	是	是	是	是	否
每粒子传输秘密信息(bit)	1	1	1	1	${\log _2}d$
量子通信协议效率(%)	14.3	19.0	16.7	28.6	28.6

DownLoad: CSV

map

[1]	Bennett C H, Brassard G, Crepeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895 Google Scholar
[2]	Li X H, Ghose S 2015 Phys. Rev. A 91 012320 Google Scholar
[3]	杨璐, 马鸿洋, 郑超, 丁晓兰, 高健存, 龙桂鲁 2017 66 230303 Google Scholar Yang L, Ma H Y, Zheng C, Ding X L, Gao J C, Long G L 2017 Acta Phys. Sin. 66 230303 Google Scholar
[4]	Vlachou C, Krawec W, Mateus P, Paunković N, Souto A 2018 Quantum Inf. Process. 17 288 Google Scholar
[5]	吴承峰, 杜亚男, 王金东, 魏正军, 秦晓娟, 赵峰, 张智明 2016 65 100302 Google Scholar Wu C F, Du Y N, Wang J D, Wei Z J, Qin X J, Zhao F, Zhang Z M 2016 Acta Phys. Sin. 65 100302 Google Scholar
[6]	安雪碧, 银振强, 韩正甫 2015 64 140303 Google Scholar An X B, Yin Z Q, Han Z F 2015 Acta Phys. Sin. 64 140303 Google Scholar
[7]	冯艳艳, 施荣华, 石金晶, 郭迎 2019 68 120302 Google Scholar Feng Y Y, Shi R H, Shi J J, Guo Y 2019 Acta Phys. Sin. 68 120302 Google Scholar
[8]	荣民希, 辛向军, 李发根 2020 69 190302 Google Scholar Rong M X, Xin X J, Li F G 2020 Acta Phys. Sin. 69 190302 Google Scholar
[9]	张沛, 周小清, 李智伟 2014 63 130301 Google Scholar Zhang P, Zhou X Q, Li Z W 2014 Acta Phys. Sin. 63 130301 Google Scholar
[10]	Chen F L, Zhang H, Chen S G, Cheng W T 2021 Quantum Inf. Process. 20 178 Google Scholar
[11]	Jiang D H, Tang K K, Xu G B 2021 Int. J. Theor. Phys. 60 4122 Google Scholar
[12]	Ma Z H, Chen J Y, Li Z, Tang C, Sua Y M, Fan H, Huang Y P 2020 Phys. Rev. Lett. 125 263602 Google Scholar
[13]	Wang Q Q, Zheng Y, Zhai C H, Li X D, Gong Q H, Wang J W 2021 J. Semicond. 42 091901 Google Scholar
[14]	Long G L, Liu X S 2002 Phys. Rev. A 65 032302 Google Scholar
[15]	Boström K, Felbinger T 2002 Phys. Rev. Lett. 89 187902 Google Scholar
[16]	Deng F G, Long G L, Liu X S 2003 Phys. Rev. A 68 042317 Google Scholar
[17]	Deng F G, Long G L 2004 Phys. Rev. A 69 052319 Google Scholar
[18]	Wang C, Deng F G, Li Y S, Liu X S, Long G L 2005 Phys. Rev. A 71 044305 Google Scholar
[19]	Shi J, Gong Y X, Xu P, Zhu S N, Zhan Y B 2011 Commun. Theor. Phys. 56 831 Google Scholar
[20]	郑晓毅龙银香 2017 66 180303 Google Scholar Zheng X Y, Long Y X 2017 Acta Phys. Sin. 66 180303 Google Scholar
[21]	Chen S S, Zhou L, Zhong W, Sheng Y B 2018 Sci. Chin. -Phys. Mech. Astron. 61 90312 Google Scholar
[22]	Gao Z K, Li T, Li Z H 2019 EPL 125 40004 Google Scholar
[23]	Zhou L, Sheng Y B, Long G L 2020 Sci. Bull. 65 12 Google Scholar
[24]	Sheng Y B, Zhou L, Long G L 2022 Sci. Bull. 67 367 Google Scholar
[25]	Hu J Y, Yu B, Jing M Y, Xiao L T, Jia S T, Qin G Q, Long G L 2016 Light Sci. Appl. 5 e16144 Google Scholar
[26]	Zhang W, Ding D S, Sheng Y B, Zhou L, Shi B S, Guo G C 2017 Phys. Rev. Lett. 118 220501 Google Scholar
[27]	Zhu F, Zhang W, Sheng Y B, Huang Y D 2017 Sci. Bull. 62 1519 Google Scholar
[28]	Qi Z T, Li Y H, Huang Y W, Feng J, Zheng Y L, Chen X F 2021 Light Sci. Appl. 10 183 Google Scholar
[29]	Boyer M, Kenigsberg D, Mor T 2007 Phys. Rev. Lett. 99 140501 Google Scholar
[30]	Zhou N R, Zhu K N, Bi W, Gong L H 2019 Quantum Inf. Process. 18 197 Google Scholar
[31]	Tsai C W, Yang C W 2021 Sci. Rep. 11 23222 Google Scholar
[32]	Han S Y, Huang Y T, Mi S, Qin X J, Wang J D, Yu Y F, Wei Z J, Zhang Z M 2021 EPJ Quantum Technol. 8 28 Google Scholar
[33]	Jiang S Q, Zhou R G, Hu W W 2021 Int. J. Theor. Phys. 60 3353 Google Scholar
[34]	Zhou N R, Xu Q D, Du N S, Gong L H 2021 Quantum Inf. Process. 20 124 Google Scholar
[35]	Ye C Q, Li J, Chen X B, Yuan T 2021 Quantum Inf. Process. 20 262 Google Scholar
[36]	Zou X F, Qiu D W 2014 Sci. Chin. -Phys. Mech. Astron. 57 1696 Google Scholar
[37]	Gu J, Lin P H, Hwang T 2018 Quantum Inf. Process. 17 182 Google Scholar
[38]	Zhang M H, Li H F, Xia Z Q, Feng X Y, Peng J Y 2017 Quantum Inf. Process. 16 117 Google Scholar
[39]	Xie C, Li L Z, Situ H Z, He J H 2018 Int. J. Theor. Phys. 57 1881 Google Scholar
[40]	Sun Y H, Yan L L, Chang Y, Zhang S B, Shao T T, Zhang Y 2019 Mod. Phys. Lett. A 34 1950004
[41]	Rong Z B, Qiu D W, Zou X F 2020 Int. J. Theor. Phys. 59 1807 Google Scholar
[42]	Ye C Q, Ye T Y, He D, Gan Z G 2019 Int. J. Theor. Phys. 58 3797 Google Scholar
[43]	Wen X J, Zhao X Q, Gong L H, Zhou N R 2019 Laser Phys. Lett. 16 075206 Google Scholar

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Vol. 71, Issue 13 - 2022-07-05

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