量子直接传态

王明宇; 王馨德; 阮东; 龙桂鲁

doi:10.7498/aps.70.20210837

摘要

把一个任意量子态在既有噪声又有窃听的信道下安全可靠地传输, 是一个广泛而重要的问题. 现在已有的方法是先传输大量的Einstein- Podolsky- Rosen (EPR)纠缠对, 然后进行纠缠纯化, 获得一对近似完美的纠缠对, 再进行隐形传态或者远程态制备来传输量子态. 本文给出一种直接安全传输量子态的方法, 通过使用量子直接通信, 安全地传输大量同样的任意量子态, 然后利用单量子态的纯化方法, 得到一个近于完美的量子态. 这是一种不需要量子纠缠的量子态安全传输方法, 避免使用纠缠资源. 这种方案是量子隐形传态和远程态制备之外的又一途径. 此外, 这一方案将原来只是用来传输经典信息的量子安全直接通信扩展到传输任意量子态的新领域, 扩大了量子直接通信的用途. 这一方案将在未来量子互联网中有重要的应用.

关键词:

Abstract

Quantum state that carries classical information, 0 or 1, can be safely and reliably transmitted using quantum secure direct communication. How to transmit an arbitrary quantum state is a wider issue and has important applications. One way is to use quantum teleportation, namely, first distribute a large number of Einstein-Podolsky-Rosen pairs, and then perform entanglement purification to obtain a near-perfect pair, and make quantum teleportation using the pair. In this article, we propose a method that directly port the quantum state with security and reliability using quantum secure direct communication. After sufficient number of copies of the same state have been directly ported, single-particle purification is performed to obtain a near perfect single particle state. This is important because it offers a new method for sending an arbitrary single particle state securely and reliably without using quantum teleportation. It is also an important extension of quantum secure direct communication to send an arbitrary quantum state. Quantum direct portation will have great potential in quantum internet.

Keywords:

quantum direct portation /
quantum secure direct communication /
quantum secure direct state transportation /
single qubit purification

作者及机构信息

1.
清华大学物理系, 低维量子物理国家重点实验室, 北京　100084

2.
清华大学教育部量子信息前沿科学中心, 北京　100084

3.
青岛大学物理科学学院, 青岛　266071

4.
北京量子信息科学研究院, 北京　100193

通信作者: 龙桂鲁, gllong@tsinghua.edu.cn

基金项目: 国家自然科学基金(批准号: 11974205)、国家高技术研究发展计划(863计划)(批准号: 2011AA06Z228)、国家重点基础研究发展计划(973计划)(批准号: 2017YFA0303700)、广东省重点研发领域研发计划(批准号: 2018B030325002)和北京未来高精尖芯片中心资助的课题

Authors and contacts

1.
State Key Laboratory of Low-Dimensional Physics, Department of Physics, Tsinghua University, Beijing 100084, China

2.
Frontiers Science Research Center, Ministry of Education, Tsinghua University, Beijing 100084, China

3.
School of Physics, Qingdao University, Qingdao 266071, China

4.
Beijing Academy of Quantum Information Sciences, Beijing 100193, China

Corresponding author: Long Gui-Lu, gllong@tsinghua.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11974205), the National High Technology Research and Development Program of China (Grant No. 2011AA06Z228), the National Basic Research Program of China (Grant No. 2017YFA0303700), the Key R&D Program of Guangdong Province, China (Grant No. 2018B030325002) and the Beijing Advanced Innovation Center for Future Chip (ICFC)

文章全文 : translate this paragraph

参考文献

[1]	Bennett C H, Brassard G 1984 Proceedings of the IEEE International Conference on Computers, Systems & Signal Processing Bangalore, India, December 10–12, 1984 p175
[2]	Zhang G, Haw J Y, Cai H, Xu F, Assad S M, Fitzsimons J F, Zhou X, Zhang Y, Yu S, Wu J, Ser W, Kwek L C, Liu A Q 2019 Nat. Photonics 13 839 Google Scholar
[3]	谷文苑, 赵尚弘, 东晨, 王星宇, 杨鼎 2019 68 240301 Google Scholar Gu W Y, Zhao S H, Dong C, Wang X Y, Yang D 2019 Acta Phys. Sin. 68 240301 Google Scholar
[4]	谷文苑, 赵尚弘, 东晨, 朱卓丹, 屈亚运 2019 68 090302 Google Scholar Gu W Y, Zhao S H, Dong C, Zhu Z D, Qu Y Y 2019 Acta Phys. Sin. 68 090302 Google Scholar
[5]	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
[6]	Wilkinson K N, Papanastasiou P, Ottaviani C, Gehring T, Pirandola1 S 2020 Phys. Rev. Res. 2 033424 Google Scholar
[7]	Valivarthi R, Etheverry S, Aldama J, Zwiehoff F, Pruneri V 2020 Opt. Express 28 14547 Google Scholar
[8]	Eriksson T A, Luís R S, Puttnam B J, Rademacher G, Fujiwara M, Awaji Y, Furukawa H, Wada N, Takeoka M, Sasaki M 2020 J. Lightwave Technol. 38 2214 Google Scholar
[9]	杜聪, 王金东, 秦晓娟, 魏正军, 於亚飞, 张智明 2020 69 190301 Google Scholar Du C, Wang J D, Qin X J, Wei Z J, Yu Y F, Zhang Z M 2020 Acta Phys. Sin. 69 190301 Google Scholar
[10]	叶炜, 郭迎, 夏莹, 钟海, 张欢, 丁建枝, 胡利云 2020 69 060301 Google Scholar Ye W, Guo Y, Xia Y, Zhong H, Zhang H, Ding J Z, Hu L Y 2020 Acta Phys. Sin. 69 060301 Google Scholar
[11]	Long G L, Liu X S 2002 Phys. Rev. A 65 032302 Google Scholar
[12]	Deng F G, Long G L, Liu X S 2003 Phys. Rev. A 68 042317 Google Scholar
[13]	Deng F G, Long G L 2004 Phys. Rev. A 69 052319 Google Scholar
[14]	Wang C, Deng F G, Li Y S, Liu X S, Long G L 2005 Phys. Rev. A 71 044305 Google Scholar
[15]	王剑, 陈皇卿, 张权, 唐朝京 2007 56 673 Google Scholar Wang J, Chen H Q, Zhang Q, Tang C J 2007 Acta Phys. Sin. 56 673 Google Scholar
[16]	王天银, 秦素娟, 温巧燕, 朱甫臣 2008 57 7452 Google Scholar Wang T Y, Qin S J, Wen Q Y, Zhu F C 2008 Acta Phys. Sin. 57 7452 Google Scholar
[17]	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
[18]	曹正文, 赵光, 张爽浩, 冯晓毅, 彭进业 2016 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
[19]	Zhu F, Zhang W, Sheng Y B, Huang Y D 2017 Sci. Bull. 62 1519 Google Scholar
[20]	Zhang W, Ding D S, Sheng Y B, Zhou L, Shi B S, Guo G C 2017 Phys. Rev. Lett. 118 220501 Google Scholar
[21]	刘志昊, 陈汉武 2017 66 130304 Google Scholar Liu Z H, Chen H W 2017 Acta Phys. Sin. 66 130304 Google Scholar
[22]	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
[23]	Qi R Y, Sun Z, Lin Z S, Niu P H, Hao W T, Song L Y, Huang Q, Gao J C, Yin L G, Long G L 2019 Light Sci. Appl. 8 22 Google Scholar
[24]	Wang C 2021 Fundamental Research 1 91 Google Scholar
[25]	Wu J W, Lin Z S, Yin L G, Long G L 2019 Quantum Eng. 1 e26
[26]	Pan D, Lin Z S, Wu J W, Zhang H R, Sun Z, Ruan D, Yin L G, Long G L 2020 Photonics Res. 8 1522 Google Scholar
[27]	Zhou Z R, Sheng Y B, Niu P H, Yin L G, Long G L, Hanzo L 2020 Sci. China-Phys. Mech. Astron. 63 230362 Google Scholar
[28]	Li T, Long G L 2020 New J. Phys. 22 063017 Google Scholar
[29]	Yang L, Wu J W, Lin Z S, Yin L G, Long G L 2020 Sci. China-Phys. Mech. Astron. 63 110311 Google Scholar
[30]	Niu P H, Wu J W, Yin L G, Long G L 2020 Quantum Inf. Process. 19 356 Google Scholar
[31]	Sun Z, Song L Y, Huang Q, Yin L G, Long G L, Lu J H, Hanzo L 2020 IEEE Trans. Commun. 68 5778 Google Scholar
[32]	Bergmann K, Theuer H, Shore B W 1998 Rev. Mod. Phys. 70 1003 Google Scholar
[33]	Vitanov N V, Halfmann T, Shore B W, Bergmann K 2001 Annu. Rev. Phys. Chem. 52 763 Google Scholar
[34]	宋克慧 2005 54 4730 Google Scholar Song K H 2005 Acta Phys. Sin. 54 4730 Google Scholar
[35]	向少华, 宋克慧 2005 54 1190 Google Scholar Xiang S H, Song K H 2005 Acta Phys. Sin. 54 1190 Google Scholar
[36]	杨雄, 童朝阳, 匡乐满 2008 57 1689 Google Scholar Yang X, Tong Z Y, Kuang L M 2008 Acta Phys. Sin. 57 1689 Google Scholar
[37]	Tian L 2012 Phys. Rev. Lett. 108 153604 Google Scholar
[38]	Wang Y D, Clerk A A 2012 Phys. Rev. Lett. 108 153603 Google Scholar
[39]	王勇, 张好, 陈杰, 王丽梅, 张临杰, 李昌勇, 赵建明, 贾锁堂 2013 62 093201 Google Scholar Wang Y, Zhang H, Chen J, Wang L M, Zhang L J, Li C Y, Zhao J M, Jia S T 2013 Acta Phys. Sin. 62 093201 Google Scholar
[40]	Chen Y H, Xia Y, Chen Q Q, Song J 2014 Phys. Rev. A 89 033856 Google Scholar
[41]	Lei F C, Gao M, Du C G, Ling J Q, Long G L 2015 Opt. Express 23 11509
[42]	Baksic A, Ribeiro H, Clerk A A 2016 Phys. Rev. Lett. 116 230503 Google Scholar
[43]	Xu X S, Zhang H, Kong X Y, Wang M, Long G L 2020 Photonics Res. 8 490 Google Scholar
[44]	Hu X M, Zhang C, Zhang C J, Liu B H, Huang Y F, Han Y J, Li C F, Guo G C 2019 Quantum Eng. 1 e13
[45]	Mastriani M, Iyengar S S 2020 Quantum Eng. 2 e55
[46]	Do H, Malaney R, Green J 2021 Quantum Eng. 3 e60
[47]	Zhou P, Lv L, He L M 2021 Quantum Eng. 3 e64
[48]	Wang T J, Yang G Q, Wang C 2020 Phys. Rev. A 101 012323 Google Scholar
[49]	Cirac J I, Ekert A K, Huelga S F, Macchiavello C 1999 Phys. Rev. A 59 4249 Google Scholar
[50]	Lim Y L, Beige A, Kwek L C 2005 Phys. Rev. Lett. 95 030505 Google Scholar
[51]	Serafini A, Mancini S, Bose S 2006 Phys. Rev. Lett. 96 010503 Google Scholar
[52]	Jiang L, Taylor J M, Sørensen A S, Lukin M D 2007 Phys. Rev. A 76 062323 Google Scholar
[53]	Feng X L, Qian J, Kwek L C, Oh C H 2008 Phys. Rev. A 78 012354 Google Scholar
[54]	van Meter R, Ladd T D, Fowler A G, Yamamoto Y 2010 Int. J. Quantum Inf. 8 295 Google Scholar
[55]	Matsuzaki Y, Benjamin S C, Fitzsimons J 2010 Phys. Rev. A 82 010302 Google Scholar
[56]	Wu C, Fang M F, Xiao X, Li Y L, Cao S 2011 Chin. Phys. B 20 020305 Google Scholar
[57]	Li Y, Benjamin S C 2012 New J. Phys. 14 093008 Google Scholar
[58]	Sheng Y B, Zhou L 2017 Sci. Bull. 62 1025 Google Scholar
[59]	Hua M, Tao M J, Alsaedi A, Hayat T, Deng F G 2018 Ann. Phys. (Berlin) 530 1700402 Google Scholar
[60]	Briegel H J, Dür W, Cirac J I, Zoller P 1998 Phys. Rev. Lett. 81 5932 Google Scholar
[61]	Bennett C H, Brassard G, Crepeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895 Google Scholar
[62]	郭弘, 李政宇, 彭翔 2016 量子密码(北京: 国防工业出版社) 第539页 Guo H, Li Z Y, Peng X 2016 Quantum Cryptography (Beijing: National Defense Industry Press) p539 (in Chinese)
[63]	Bennett C H, Brassard G, Popescu S, Schumacher B, Smolin J A, Wootters W K 1996 Phys. Rev. Lett. 76 722 Google Scholar
[64]	Lo H K 2000 Phys. Rev. A 62 012313 Google Scholar
[65]	Pati A K 2020 Phys. Rev. A 63 014302
[66]	Bennett C H, DiVincenzo D P, Shor P W, Smolin J A, Terhal B M, Wootters W K 2001 Phys. Rev. Lett. 87 077902 Google Scholar
[67]	Cirac J I, Ekert A K, Macchiavello C 1999 Phys. Rev. Lett. 82 4344 Google Scholar
[68]	Ricci M, De Martini F, Cerf N J, Filip R, Fiurášek J, Macchiavello C 2004 Phys. Rev. Lett. 93 170501 Google Scholar
[69]	Hou S Y, Sheng Y B, Feng G R, Long G L 2014 Sci. Rep. 4 6857
[70]	Han C, Zhou Z W, Guo G C 2006 J. Phys. B:At. Mol. Opt. Phys. 39 1677 Google Scholar
[71]	邓富国, 李熙涵, 李涛 2018 67 130301 Google Scholar Deng F G, Li X H, Li T 2018 Acta Phys. Sin. 67 130301 Google Scholar
[72]	孙越 2013 量子光学学报 19 122 Sun Y 2013 Acta Sin. Quantum Opt. 19 122
[73]	Sheng Y B, Zhou L 2018 Phys. Rev. A 98 052343 Google Scholar
[74]	Qin W, Wang C, Cao Y, Long G L 2014 Phys. Rev. A 89 062314 Google Scholar

施引文献

表 1 $ {\boldsymbol{U}}_{\varphi } $操作前后序列B中的单光子态(传输任意已知单比特量子态)

Table 1. Single photon states in sequence B before and after $ {\boldsymbol{U}}_{\varphi } $ operation in the case of transmitting arbitrary known single qubit.

$ {\boldsymbol{U}}_{\varphi } $操作前	$ {\boldsymbol{U}}_{\varphi } $操作后
$\|0 \rangle$	$ a\|0 \rangle +b\|1 \rangle $
$ \|1 \rangle $	$ -{b}^{*}\left\|0 \rangle +a\right\|1 \rangle $
$ \|+ \rangle $	$({1}/{\sqrt{2} })[\left(a-{b}^{*}\right)\left\|0 \rangle +\left(a+b\right)\right\|1 \rangle ]$
$ \|- \rangle $	$({1}/{\sqrt{2} })[\left(a+{b}^{*}\right)\left\|0 \rangle +\left(b-a\right)\right\|1 \rangle ]$

下载: 导出CSV

表 2 $ {\boldsymbol{U}}_{\varphi } $操作前后序列B中的单光子态和Bob采用的操作(传输赤道态)

Table 2. Single photon states in sequence B before and after $ {\boldsymbol{U}}_{\varphi } $ operation in the case of transmitting equatorial state & Bob’s related operations.

$ {\boldsymbol{U}}_{\varphi } $操作前	$ {\boldsymbol{U}}_{\varphi } $操作后	Bob采用的操作
$ \|0 \rangle $	$ \|0 \rangle $	舍弃
$ \|1 \rangle $	$ {{\rm{e}}}^{{\rm{i}}\phi }\|1 \rangle $	舍弃
$ \|+ \rangle $	$({1}/{\sqrt{2} })\left(\right\|0 \rangle +{ {\rm{e} } }^{ {\rm{i} }\phi }\|1 \rangle )$	I
$ \|- \rangle $	$({1}/{\sqrt{2} })\left(\right\|0 \rangle -{ {\rm{e} } }^{ {\rm{i} }\phi }\left\|1 \rangle \right)$	Z

下载: 导出CSV

表 3 $ {\boldsymbol{U}}_{\varphi } $操作前后序列B中的单光子态和Bob采用的操作(传输实系数态)

Table 3. Single photon states in sequence B before and after $ {\boldsymbol{U}}_{\varphi } $ operation in the case of transmitting real-coefficient state & Bob’s related operations.

$ {\boldsymbol{U}}_{\varphi } $操作前	$ {\boldsymbol{U}}_{\varphi } $操作后	Bob采用的操作
$ \|0 \rangle $	$ a\|0 \rangle +b\|1 \rangle $	I
$ \|1 \rangle $	$ -b\|0 \rangle +a\|1 \rangle $	Y
$ \|+ \rangle $	$({1}/{\sqrt{2} })[\left(a-b\right)\left\|0 \rangle +\left(a+b\right)\right\|1 \rangle ]$	$ ZH $
$ \|- \rangle $	$({1}/{\sqrt{2} })[\left(a+b\right)\left\|0 \rangle +\left(b-a\right)\right\|1 \rangle ]$	$ XH $

下载: 导出CSV

map

[1]	Bennett C H, Brassard G 1984 Proceedings of the IEEE International Conference on Computers, Systems & Signal Processing Bangalore, India, December 10–12, 1984 p175
[2]	Zhang G, Haw J Y, Cai H, Xu F, Assad S M, Fitzsimons J F, Zhou X, Zhang Y, Yu S, Wu J, Ser W, Kwek L C, Liu A Q 2019 Nat. Photonics 13 839 Google Scholar
[3]	谷文苑, 赵尚弘, 东晨, 王星宇, 杨鼎 2019 68 240301 Google Scholar Gu W Y, Zhao S H, Dong C, Wang X Y, Yang D 2019 Acta Phys. Sin. 68 240301 Google Scholar
[4]	谷文苑, 赵尚弘, 东晨, 朱卓丹, 屈亚运 2019 68 090302 Google Scholar Gu W Y, Zhao S H, Dong C, Zhu Z D, Qu Y Y 2019 Acta Phys. Sin. 68 090302 Google Scholar
[5]	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
[6]	Wilkinson K N, Papanastasiou P, Ottaviani C, Gehring T, Pirandola1 S 2020 Phys. Rev. Res. 2 033424 Google Scholar
[7]	Valivarthi R, Etheverry S, Aldama J, Zwiehoff F, Pruneri V 2020 Opt. Express 28 14547 Google Scholar
[8]	Eriksson T A, Luís R S, Puttnam B J, Rademacher G, Fujiwara M, Awaji Y, Furukawa H, Wada N, Takeoka M, Sasaki M 2020 J. Lightwave Technol. 38 2214 Google Scholar
[9]	杜聪, 王金东, 秦晓娟, 魏正军, 於亚飞, 张智明 2020 69 190301 Google Scholar Du C, Wang J D, Qin X J, Wei Z J, Yu Y F, Zhang Z M 2020 Acta Phys. Sin. 69 190301 Google Scholar
[10]	叶炜, 郭迎, 夏莹, 钟海, 张欢, 丁建枝, 胡利云 2020 69 060301 Google Scholar Ye W, Guo Y, Xia Y, Zhong H, Zhang H, Ding J Z, Hu L Y 2020 Acta Phys. Sin. 69 060301 Google Scholar
[11]	Long G L, Liu X S 2002 Phys. Rev. A 65 032302 Google Scholar
[12]	Deng F G, Long G L, Liu X S 2003 Phys. Rev. A 68 042317 Google Scholar
[13]	Deng F G, Long G L 2004 Phys. Rev. A 69 052319 Google Scholar
[14]	Wang C, Deng F G, Li Y S, Liu X S, Long G L 2005 Phys. Rev. A 71 044305 Google Scholar
[15]	王剑, 陈皇卿, 张权, 唐朝京 2007 56 673 Google Scholar Wang J, Chen H Q, Zhang Q, Tang C J 2007 Acta Phys. Sin. 56 673 Google Scholar
[16]	王天银, 秦素娟, 温巧燕, 朱甫臣 2008 57 7452 Google Scholar Wang T Y, Qin S J, Wen Q Y, Zhu F C 2008 Acta Phys. Sin. 57 7452 Google Scholar
[17]	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
[18]	曹正文, 赵光, 张爽浩, 冯晓毅, 彭进业 2016 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
[19]	Zhu F, Zhang W, Sheng Y B, Huang Y D 2017 Sci. Bull. 62 1519 Google Scholar
[20]	Zhang W, Ding D S, Sheng Y B, Zhou L, Shi B S, Guo G C 2017 Phys. Rev. Lett. 118 220501 Google Scholar
[21]	刘志昊, 陈汉武 2017 66 130304 Google Scholar Liu Z H, Chen H W 2017 Acta Phys. Sin. 66 130304 Google Scholar
[22]	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
[23]	Qi R Y, Sun Z, Lin Z S, Niu P H, Hao W T, Song L Y, Huang Q, Gao J C, Yin L G, Long G L 2019 Light Sci. Appl. 8 22 Google Scholar
[24]	Wang C 2021 Fundamental Research 1 91 Google Scholar
[25]	Wu J W, Lin Z S, Yin L G, Long G L 2019 Quantum Eng. 1 e26
[26]	Pan D, Lin Z S, Wu J W, Zhang H R, Sun Z, Ruan D, Yin L G, Long G L 2020 Photonics Res. 8 1522 Google Scholar
[27]	Zhou Z R, Sheng Y B, Niu P H, Yin L G, Long G L, Hanzo L 2020 Sci. China-Phys. Mech. Astron. 63 230362 Google Scholar
[28]	Li T, Long G L 2020 New J. Phys. 22 063017 Google Scholar
[29]	Yang L, Wu J W, Lin Z S, Yin L G, Long G L 2020 Sci. China-Phys. Mech. Astron. 63 110311 Google Scholar
[30]	Niu P H, Wu J W, Yin L G, Long G L 2020 Quantum Inf. Process. 19 356 Google Scholar
[31]	Sun Z, Song L Y, Huang Q, Yin L G, Long G L, Lu J H, Hanzo L 2020 IEEE Trans. Commun. 68 5778 Google Scholar
[32]	Bergmann K, Theuer H, Shore B W 1998 Rev. Mod. Phys. 70 1003 Google Scholar
[33]	Vitanov N V, Halfmann T, Shore B W, Bergmann K 2001 Annu. Rev. Phys. Chem. 52 763 Google Scholar
[34]	宋克慧 2005 54 4730 Google Scholar Song K H 2005 Acta Phys. Sin. 54 4730 Google Scholar
[35]	向少华, 宋克慧 2005 54 1190 Google Scholar Xiang S H, Song K H 2005 Acta Phys. Sin. 54 1190 Google Scholar
[36]	杨雄, 童朝阳, 匡乐满 2008 57 1689 Google Scholar Yang X, Tong Z Y, Kuang L M 2008 Acta Phys. Sin. 57 1689 Google Scholar
[37]	Tian L 2012 Phys. Rev. Lett. 108 153604 Google Scholar
[38]	Wang Y D, Clerk A A 2012 Phys. Rev. Lett. 108 153603 Google Scholar
[39]	王勇, 张好, 陈杰, 王丽梅, 张临杰, 李昌勇, 赵建明, 贾锁堂 2013 62 093201 Google Scholar Wang Y, Zhang H, Chen J, Wang L M, Zhang L J, Li C Y, Zhao J M, Jia S T 2013 Acta Phys. Sin. 62 093201 Google Scholar
[40]	Chen Y H, Xia Y, Chen Q Q, Song J 2014 Phys. Rev. A 89 033856 Google Scholar
[41]	Lei F C, Gao M, Du C G, Ling J Q, Long G L 2015 Opt. Express 23 11509
[42]	Baksic A, Ribeiro H, Clerk A A 2016 Phys. Rev. Lett. 116 230503 Google Scholar
[43]	Xu X S, Zhang H, Kong X Y, Wang M, Long G L 2020 Photonics Res. 8 490 Google Scholar
[44]	Hu X M, Zhang C, Zhang C J, Liu B H, Huang Y F, Han Y J, Li C F, Guo G C 2019 Quantum Eng. 1 e13
[45]	Mastriani M, Iyengar S S 2020 Quantum Eng. 2 e55
[46]	Do H, Malaney R, Green J 2021 Quantum Eng. 3 e60
[47]	Zhou P, Lv L, He L M 2021 Quantum Eng. 3 e64
[48]	Wang T J, Yang G Q, Wang C 2020 Phys. Rev. A 101 012323 Google Scholar
[49]	Cirac J I, Ekert A K, Huelga S F, Macchiavello C 1999 Phys. Rev. A 59 4249 Google Scholar
[50]	Lim Y L, Beige A, Kwek L C 2005 Phys. Rev. Lett. 95 030505 Google Scholar
[51]	Serafini A, Mancini S, Bose S 2006 Phys. Rev. Lett. 96 010503 Google Scholar
[52]	Jiang L, Taylor J M, Sørensen A S, Lukin M D 2007 Phys. Rev. A 76 062323 Google Scholar
[53]	Feng X L, Qian J, Kwek L C, Oh C H 2008 Phys. Rev. A 78 012354 Google Scholar
[54]	van Meter R, Ladd T D, Fowler A G, Yamamoto Y 2010 Int. J. Quantum Inf. 8 295 Google Scholar
[55]	Matsuzaki Y, Benjamin S C, Fitzsimons J 2010 Phys. Rev. A 82 010302 Google Scholar
[56]	Wu C, Fang M F, Xiao X, Li Y L, Cao S 2011 Chin. Phys. B 20 020305 Google Scholar
[57]	Li Y, Benjamin S C 2012 New J. Phys. 14 093008 Google Scholar
[58]	Sheng Y B, Zhou L 2017 Sci. Bull. 62 1025 Google Scholar
[59]	Hua M, Tao M J, Alsaedi A, Hayat T, Deng F G 2018 Ann. Phys. (Berlin) 530 1700402 Google Scholar
[60]	Briegel H J, Dür W, Cirac J I, Zoller P 1998 Phys. Rev. Lett. 81 5932 Google Scholar
[61]	Bennett C H, Brassard G, Crepeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895 Google Scholar
[62]	郭弘, 李政宇, 彭翔 2016 量子密码(北京: 国防工业出版社) 第539页 Guo H, Li Z Y, Peng X 2016 Quantum Cryptography (Beijing: National Defense Industry Press) p539 (in Chinese)
[63]	Bennett C H, Brassard G, Popescu S, Schumacher B, Smolin J A, Wootters W K 1996 Phys. Rev. Lett. 76 722 Google Scholar
[64]	Lo H K 2000 Phys. Rev. A 62 012313 Google Scholar
[65]	Pati A K 2020 Phys. Rev. A 63 014302
[66]	Bennett C H, DiVincenzo D P, Shor P W, Smolin J A, Terhal B M, Wootters W K 2001 Phys. Rev. Lett. 87 077902 Google Scholar
[67]	Cirac J I, Ekert A K, Macchiavello C 1999 Phys. Rev. Lett. 82 4344 Google Scholar
[68]	Ricci M, De Martini F, Cerf N J, Filip R, Fiurášek J, Macchiavello C 2004 Phys. Rev. Lett. 93 170501 Google Scholar
[69]	Hou S Y, Sheng Y B, Feng G R, Long G L 2014 Sci. Rep. 4 6857
[70]	Han C, Zhou Z W, Guo G C 2006 J. Phys. B:At. Mol. Opt. Phys. 39 1677 Google Scholar
[71]	邓富国, 李熙涵, 李涛 2018 67 130301 Google Scholar Deng F G, Li X H, Li T 2018 Acta Phys. Sin. 67 130301 Google Scholar
[72]	孙越 2013 量子光学学报 19 122 Sun Y 2013 Acta Sin. Quantum Opt. 19 122
[73]	Sheng Y B, Zhou L 2018 Phys. Rev. A 98 052343 Google Scholar
[74]	Qin W, Wang C, Cao Y, Long G L 2014 Phys. Rev. A 89 062314 Google Scholar

[1]	刘启沛, 张程贤, 薛正远. 强驱动单态-三重态量子比特的高保真单比特门. , 2023, 72(20): 200302. doi: 10.7498/aps.72.20230906
[2]	周贤韬, 江英华, 郭晓军, 彭展. 带双向身份认证的基于单光子和Bell态混合的量子安全直接通信方案. , 2023, 72(13): 130302. doi: 10.7498/aps.72.20221972
[3]	周贤韬, 江英华. 带身份认证的量子安全直接通信方案. , 2023, 72(2): 020302. doi: 10.7498/aps.72.20221684
[4]	危语嫣, 高子凯, 王思颖, 朱雅静, 李涛. 基于单光子双量子态的确定性安全量子通信. , 2022, 71(5): 050302. doi: 10.7498/aps.71.20210907
[5]	龚黎华, 陈振泳, 徐良超, 周南润. 基于高维单粒子态的双向半量子安全直接通信协议. , 2022, 71(13): 130304. doi: 10.7498/aps.71.20211702
[6]	赵宁, 江英华, 周贤韬. 基于单光子的高效量子安全直接通信方案. , 2022, 71(15): 150304. doi: 10.7498/aps.71.20220202
[7]	危语嫣, 高子凯, 王思颖, 朱雅静, 李涛. 基于单光子双量子态的确定性的安全量子通讯. , 2021, (): . doi: 10.7498/aps.70.20210907
[8]	郑晓毅, 龙银香. 基于cluster态的信道容量可控的可控量子安全直接通信方案. , 2017, 66(18): 180303. doi: 10.7498/aps.66.180303
[9]	杨璐, 马鸿洋, 郑超, 丁晓兰, 高健存, 龙桂鲁. 基于量子隐形传态的量子保密通信方案. , 2017, 66(23): 230303. doi: 10.7498/aps.66.230303
[10]	刘志昊, 陈汉武. 基于Bell态粒子和单光子混合的量子安全直接通信方案的信息泄露问题. , 2017, 66(13): 130304. doi: 10.7498/aps.66.130304
[11]	曹正文, 赵光, 张爽浩, 冯晓毅, 彭进业. 基于Bell态粒子和单光子混合的量子安全直接通信方案. , 2016, 65(23): 230301. doi: 10.7498/aps.65.230301
[12]	李熙涵. 量子直接通信. , 2015, 64(16): 160307. doi: 10.7498/aps.64.160307
[13]	马鸿洋, 秦国卿, 范兴奎, 初鹏程. 噪声情况下的量子网络直接通信. , 2015, 64(16): 160306. doi: 10.7498/aps.64.160306
[14]	乔盼盼, 艾合买提·阿不力孜, 蔡江涛, 路俊哲, 麦麦提依明·吐孙, 日比古·买买提明. 利用热平衡态超导电荷量子比特实现量子隐形传态. , 2012, 61(24): 240303. doi: 10.7498/aps.61.240303
[15]	何锐, Bing He. 量子隐形传态的新方案. , 2011, 60(6): 060302. doi: 10.7498/aps.60.060302
[16]	权东晓, 裴昌幸, 刘丹, 赵楠. 基于单光子的单向量子安全通信协议. , 2010, 59(4): 2493-2497. doi: 10.7498/aps.59.2493
[17]	王天银, 秦素娟, 温巧燕, 朱甫臣. 多方控制的量子安全直接通信协议的分析及改进. , 2008, 57(12): 7452-7456. doi: 10.7498/aps.57.7452
[18]	杜建忠, 陈秀波, 温巧燕, 朱甫臣. 保密多方量子求和. , 2007, 56(11): 6214-6219. doi: 10.7498/aps.56.6214
[19]	王剑, 陈皇卿, 张权, 唐朝京. 多方控制的量子安全直接通信协议. , 2007, 56(2): 673-677. doi: 10.7498/aps.56.673
[20]	刘传龙, 郑亦庄. 纠缠相干态的量子隐形传态. , 2006, 55(12): 6222-6228. doi: 10.7498/aps.55.6222

计量

文章访问数: 5264
PDF下载量: 157
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

$ {\boldsymbol{U}}_{\varphi } $操作前	$ {\boldsymbol{U}}_{\varphi } $操作后
$\|0 \rangle$	$ a\|0 \rangle +b\|1 \rangle $
$ \|1 \rangle $	$ -{b}^{*}\left\|0 \rangle +a\right\|1 \rangle $
$ \|+ \rangle $	$({1}/{\sqrt{2} })[\left(a-{b}^{*}\right)\left\|0 \rangle +\left(a+b\right)\right\|1 \rangle ]$
$ \|- \rangle $	$({1}/{\sqrt{2} })[\left(a+{b}^{*}\right)\left\|0 \rangle +\left(b-a\right)\right\|1 \rangle ]$

$ {\boldsymbol{U}}_{\varphi } $操作前	$ {\boldsymbol{U}}_{\varphi } $操作后	Bob采用的操作
$ \|0 \rangle $	$ \|0 \rangle $	舍弃
$ \|1 \rangle $	$ {{\rm{e}}}^{{\rm{i}}\phi }\|1 \rangle $	舍弃
$ \|+ \rangle $	$({1}/{\sqrt{2} })\left(\right\|0 \rangle +{ {\rm{e} } }^{ {\rm{i} }\phi }\|1 \rangle )$	I
$ \|- \rangle $	$({1}/{\sqrt{2} })\left(\right\|0 \rangle -{ {\rm{e} } }^{ {\rm{i} }\phi }\left\|1 \rangle \right)$	Z

$ {\boldsymbol{U}}_{\varphi } $操作前	$ {\boldsymbol{U}}_{\varphi } $操作后	Bob采用的操作
$ \|0 \rangle $	$ a\|0 \rangle +b\|1 \rangle $	I
$ \|1 \rangle $	$ -b\|0 \rangle +a\|1 \rangle $	Y
$ \|+ \rangle $	$({1}/{\sqrt{2} })[\left(a-b\right)\left\|0 \rangle +\left(a+b\right)\right\|1 \rangle ]$	$ ZH $
$ \|- \rangle $	$({1}/{\sqrt{2} })[\left(a+b\right)\left\|0 \rangle +\left(b-a\right)\right\|1 \rangle ]$	$ XH $

搜索

留言板