Deterministic secure quantum communication with double-encoded single photons

Wei Yu-Yan; Gao Zi-Kai; Wang Si-Ying; Zhu Ya-Jing; Li Tao

doi:10.7498/aps.71.20210907

Abstract

Quantum communication is an important branch of quantum technology. It can safely transmit private information between legitimate parties and its unconditional security is guaranteed by quantum physics. So far, deterministic secure quantum communication without entanglement usually transmits single photons in two-way quantum channels. We propose a deterministic secure quantum communication proposal, and it requires a one-way quantum channel and a classical channel. In our protocol, a sender encodes logical bits by using two conjugate bases consisting of the polarization and time-bin degrees of freedom of a photon and transmits it to a receiver over a quantum channel. Upon receiving this photon, the receiver measures it randomly in two bases and can decode the bit deterministically with the help of the sender. Any attack from eavesdroppers will be detected by the legitimate parties. Furthermore, this protocol can be implemented with linear-optic elements and single-photon detectors.

Keywords:

Authors and contacts

1.
School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
2.
MIIT Key Laboratory of Semiconductor Microstructure, Nanjing University of Science and Technology, Nanjing 210094, China

Corresponding author: Li Tao, tao.li@njust.edu.cn

Funds: Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20180461) and the National Natural Science Foundation of China (Grant No. 11914171)

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References

[1]	Wehner S, Elkouss D, Hanso R 2018 Science 362 eaam9288 Google Scholar
[2]	Bennett C H, Brassard G 1984 Proceedings of the IEEE International Conference on Computers, Systems & Signal Processing Bangalore, India, December 10–12, 1984 p175
[3]	Ekert A K 1991 Phys. Rev. Lett. 67 661 Google Scholar
[4]	Bennett C H 1992 Phys. Rev. Lett. 68 3121 Google Scholar
[5]	Guo P L, Dong C, He Y, Jing F, He W T, Ren B C, Li C Y, Deng F G 2020 Opt. Express 28 4611 Google Scholar
[6]	Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145 Google Scholar
[7]	Long G L, Liu X S 2002 Phys. Rev. A 65 032302 Google Scholar
[8]	Deng F G, Long G L, Liu X S 2003 Phys. Rev. A 68 042317 Google Scholar
[9]	Deng F G, Long G L 2004 Phys. Rev. A 69 052319 Google Scholar
[10]	Wang C, Deng F G, Li Y S, Liu X S, Long G L 2005 Phys. Rev. A 71 044305 Google Scholar
[11]	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
[12]	Zhang W, Ding D S, Sheng Y B, Zhou L, Shi B S, Guo G C 2017 Phys. Rev. Lett. 118 220501 Google Scholar
[13]	Li T, Gao Z K, Li Z H 2020 EPL 131 60001 Google Scholar
[14]	Gao Z K, Li T, Li Z H 2019 EPL 125 40004 Google Scholar
[15]	Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1829 Google Scholar
[16]	Karlsson A, Koashi M, Imoto N 1999 Phys Rev. A 59 162 Google Scholar
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[18]	Gao Z K, Li T, Li Z H 2020 Sci. Chin. -Phys. Mech. Astron. 63 120311 Google Scholar
[19]	Shimizu K, Imoto Y 1999 Phys. Rev. A 60 157 Google Scholar
[20]	Boström K, Felbinger T 2002 Phys. Rev. Lett. 89 187902 Google Scholar
[21]	Cai Q Y, Li B W 2004 Chin. Phys. Lett. 21 601 Google Scholar
[22]	Wójcik A 2003 Phys. Rev. Lett. 90 157901 Google Scholar
[23]	Long G L, Deng F G, Wang C, Li X H, Wen K, Wang W Y 2007 Front. Phys. Chin. 2 251
[24]	Li T, Long G L 2020 New J. Phys. 22 063017 Google Scholar
[25]	王明宇, 王馨德, 阮东, 龙桂鲁 2021 70 190301 Google Scholar Wang M Y, Wang X D, Ruan D, Long G L 2021 Acta Phys. Sin. 70 190301 Google Scholar
[26]	窦建鹏, 李航, 庞晓玲, 张超妮, 杨天怀, 金贤敏 2019 68 030307 Google Scholar Dou J P, Li H, Pang X L, Zhang C N, Yang T H, Jin X M 2019 Acta Phys. Sin. 68 030307 Google Scholar
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[28]	Cai Q Y, Li B W 2004 Phys. Rev. A 69 054301 Google Scholar
[29]	Gao T, Yan F L, Wang Z X 2005 J. Phys. A:Gen. Phys. 38 5761 Google Scholar
[30]	Elsayed T A 2020 Phys. Scr. 96 025101 Google Scholar
[31]	Jeong Y C, Ji S W, Hong C, Park H S, Jang J 2020 Entropy 22 1268 Google Scholar
[32]	Jiang D, Chen Y, Gu X, Xie L, Chen L 2017 Sci. Rep. 7 44934 Google Scholar
[33]	Wang J D, Wei Z J, Zhang H, Qin X J, Liu X B, Zhang Z M, Liao C J, Liu S H 2010 J. Phys. B:At. Mol. Opt. Phys. 43 095504 Google Scholar
[34]	Lu H, Fung C, Ma X, Cai QY 2011 Phys. Rev. A 84 042344 Google Scholar
[35]	Beaudry N J, Lucamarini M, Mancini S, Renner R 2013 Phys. Rev. A 88 062302 Google Scholar
[36]	Henao C I, Serra R M 2015 Phys. Rev. A 92 052317 Google Scholar
[37]	Xu F, Ma X, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002 Google Scholar
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[42]	Wang H, Li W, Jiang X, He Y M, Li Y H, Ding X, Chen M C, Qin J, Peng C Z, Schneider C, Kamp M, Zhang W J, Li H, You L X, Wang Z, Dowling J P, Höfling S, Lu C Y, Pan J W 2018 Phys. Rev. Lett. 120 230502 Google Scholar
[43]	Deng F G, Ren B C, Li X H 2017 Sci. Bull. 62 46 Google Scholar
[44]	Erhard M, Krenn M, Zeilinger A 2020 Nat. Rev. Phys. 2 365 Google Scholar
[45]	郭邦红, 杨理, 向憧, 关翀, 吴令安, 刘颂豪 2013 62 130303 Google Scholar Guo B H, Yang L, Xiang C, Guan C, Wu L A, Liu S H 2013 Acta Phys. Sin. 62 130303 Google Scholar

Cited By

图 1 量子逻辑比特制备示意图. HWP: 半波片, 光轴与水平方向的夹角$ \theta = 0 $, 穿过它的光子极化状态保持不变, $ \theta = $$ {\text{π}}/4 $, 对穿过它的光子执行以下操作: $\left| H \right\rangle \to \left| V \right\rangle, \;\left| V \right\rangle \to $$ \left| H \right\rangle$; $ {\text{SW}}i \left( {i = 1, \;2, \;3} \right) $: 开关, 处于T状态时, 光子直接透过器件, 处于R状态时, 光子将被反射; H1: 光轴角度为$ {\text{π}}/8 $的半波片, 对经过的光子进行以下操作: $\left| H \right\rangle \to \left| + \right\rangle, \left| V \right\rangle \to $$ \left| - \right\rangle$; $ {{{\rm{PBS1}}, \;{\rm{PBS2}}}} $: 极化分束器, 将透射$ \left| + \right\rangle $光子, 反射$ \left| - \right\rangle $光子; PM: 相位调制器, 产生$ \varphi = 0 $或$ \varphi = {\text{π}} $的相位差; BS1: 50∶50分束器

Figure 1. Schematics of quantum logic qubit preparation. HWP: half wave plate with its axis aligned at $ \theta = 0 $($\theta = $$ {\text{π}}/4$) completes the transformations $ |H\rangle \to |H\rangle, |V\rangle \to |V\rangle $ ($ |H\rangle \to |V\rangle, |V\rangle \to |H\rangle $); $ {\text{SW}}i \left( {i = 1, \;2, \;3} \right) $: optical switch transmits (reflects) photons when it is set to modeT(R); H1 with its axis aligned at $ {\text{π}}/8 $completes the following transmissions: $ |H\rangle \to |+\rangle, |V\rangle \to |-\rangle $; $ {\text{PBS1}}\;{\text{and}}\;{\text{PBS2}} $: polarizing beam splitters that transmit (reflect) photons in state $ \left| + \right\rangle $($ \left| - \right\rangle $); PM: a phase modulator which introduces a phase $\varphi =0$ or $\varphi ={{ {\text{π}} }}$; BS1 : 50∶50 beam splitter.

DownLoad: Full-Size Img PowerPoint

图 2 量子逻辑比特解码示意图. BS2: 50:50分束器; SW4: 开关, 透射$ {t_1} $模式的光子, 反射$ {t_0} $模式的光子; ${\rm{PBS3}}, \; {\rm{PBS4}}, $$ \;{\rm{PBS5}}, \;{\rm{PBS6}}$: 极化分束器($ {{{\rm{PBS3}}, \;{\rm{PBS4}}}} $透射$ \left| H \right\rangle $光子, 反射$ \left| V \right\rangle $光子, $ {{{\rm{PBS5}}, \;{\rm{PBS6}}}} $透射$ \left| {{ + }} \right\rangle $光子, 反射$ \left| - \right\rangle $光子); HWPS: 半波片, 将对光子进行如下操作: $ \left| H \right\rangle \to \left| V \right\rangle $, $ \left| V \right\rangle \to - \left| H \right\rangle $, $ \left| + \right\rangle \to \left| - \right\rangle $, $ \left| - \right\rangle \to - \left| + \right\rangle $; $ {\text{H2}}, \;{\rm{H3}} $: 光轴角度为$ {{{\text{π}} /8}} $的半波片, 对经过的光子进行以下操作: $ \left| H \right\rangle \to \left| + \right\rangle, \;\left| V \right\rangle \to \left| - \right\rangle $; ${{\rm{D}}_i}(i = 1, \cdots, 6)$: 单光子探测器.

Figure 2. Schematics of quantum logic qubit measurement. BS2: 50:50 beam splitter; SW4: switch transmits photons in $ {t_1} $ mode and reflects photons in $ {t_0} $ mode; ${\text{PBS3}}, \;{\text{PBS4}}, $$ \; {\text{PBS5}} \;{\text{and}}\;{\text{PBS6}}$: polarizing beam splitters. PBS3 and PBS4 transmit (reflect) photons in state $ \left| H \right\rangle $($ \left| V \right\rangle $). $ {\text{PBS5}}\;{\text{and}}\;{\text{PBS6}} $ transmit (reflect) photons in state $ \left| + \right\rangle $($ \left| - \right\rangle $). HWPS: half wave plate transforms the polarization of a photon passing it as follows:$ |H\rangle \to |V\rangle, |V\rangle \to -|H\rangle$, $ |+\rangle \to |-\rangle, |-\rangle \to -|+\rangle $. $ {\text{H2}}\;{\text{and}}\;{\text{H3}} $ with their axes aligned at $ {\text{π}}/8 $complete the following transmissions:$ |H\rangle \to |+\rangle, |V\rangle \to |-\rangle $.${{\rm{D}}_i}\;(i = 1,\cdots, 6)$: single-photon detectors.

DownLoad: Full-Size Img PowerPoint

表 1 四种单光子态对应的探测器响应情况

Table 1. Clicks of detectors for four different single-photon states.

量子态	下路径	右路径
$ \left\| {H{t_{{ + }}}} \right\rangle $	$ {D_1}\left( {{t_0}} \right)/{D_1}\left( {{t_1}} \right) $	$ {D_3}\left( {{t_1}} \right)/{D_6}\left( {{t_1}} \right) $
$ \left\| {V{t_ - }} \right\rangle $	$ {D_2}\left( {{t_0}} \right)/{D_2}\left( {{t_1}} \right) $	$ {D_4}\left( {{t_1}} \right)/{D_5}\left( {{t_1}} \right) $
$ \left\| { + {t_0}} \right\rangle $	$ {D_1}\left( {{t_0}} \right)/{D_2}\left( {{t_0}} \right) $	$ {D_5}\left( {{t_1}} \right)/{D_6}\left( {{t_1}} \right) $
$ \left\| { - {t_0}} \right\rangle $	$ {D_1}\left( {{t_1}} \right)/{D_2}\left( {{t_1}} \right) $	$ {D_3}\left( {{t_1}} \right)/{D_4}\left( {{t_1}} \right) $

DownLoad: CSV

表 2 Bob探测器响应的可能情况

Table 2. Click probability of Bob’s detectors.

响应	$ {D_1}\left( {{t_0}} \right) $	$ {D_1}\left( {{t_1}} \right) $	$ {D_3}\left( {{t_1}} \right) $	$ {D_6}\left( {{t_1}} \right) $
概率	$ {1}/{4} $	$ {1}/{4} $	$ {1}/{4} $	$ {1}/{4} $

DownLoad: CSV

表 3 Eve制备的光子态及概率

Table 3. State and probability of photons prepared by Eve.

光子态	$ \left\| {H{t_ + }} \right\rangle $	$ \left\| { + {t_0}} \right\rangle $	$ \left\| { - {t_1}} \right\rangle $
概率	$ {1}/{2} $	$ {1}/{4} $	$ {1}/{4} $

DownLoad: CSV

表 4 Eve制备的光子引起的探测器响应的可能情况

Table 4. Click and probability of detectors triggered by Eve’s photon.

探测器响应	$ {D_1}\left( {{t_0}} \right) $	$ {D_1}\left( {{t_1}} \right) $	$ {D_3}\left( {{t_1}} \right) $	$ {D_6}\left( {{t_1}} \right) $	$ {D_2}\left( {{t_0}} \right) $	$ {D_2}\left( {{t_1}} \right) $	$ {D_4}\left( {{t_1}} \right) $	$ {D_5}\left( {{t_1}} \right) $
概率	$ {3}/{{16}} $	$ {3}/{{16}} $	$ {3}/{{16}} $	$ {3}/{{16}} $	$ {1}/{{16}} $	$ {1}/{{16}} $	$ {1}/{{16}} $	$ {1}/{{16}} $

DownLoad: CSV

表 5 Bob探测器响应的可能情况

Table 5. Click probability of Bob’s detectors.

响应	$ {D_2}\left( {{t_0}} \right) $	$ {D_2}\left( {{t_1}} \right) $	$ {D_4}\left( {{t_1}} \right) $	$ {D_5}\left( {{t_1}} \right) $
概率	$1/{4}$	$1/{4}$	$1/{4}$	$1/{4}$

DownLoad: CSV

表 6 Eve制备的光子态及概率

Table 6. State and probability of photons prepared by Eve.

光子态	$ \left\| {V{t_ - }} \right\rangle $	$ \left\| { + {t_0}} \right\rangle $	$ \left\| { - {t_1}} \right\rangle $
概率	$1/{2}$	$1/{4}$	$1/{4}$

DownLoad: CSV

表 7 Eve制备的光子引起的探测器响应的可能情况

Table 7. Click and probability of detectors triggered by Eve’s photon.

探测器响应		$ {D_2}\left( {{t_0}} \right) $	$ {D_2}\left( {{t_1}} \right) $	$ {D_4}\left( {{t_1}} \right) $	$ {D_5}\left( {{t_1}} \right) $	$ {D_1}\left( {{t_0}} \right) $	$ {D_1}\left( {{t_1}} \right) $	$ {D_3}\left( {{t_1}} \right) $	$ {D_6}\left( {{t_1}} \right) $
概率	$ {3}/{{16}} $		$ {3}/{{16}} $	$ {3}/{{16}} $	$ {3}/{{16}} $	$ {1}/{{16}} $	$ {1}/{{16}} $	$ {1}/{{16}} $	$ {1}/{{16}} $

DownLoad: CSV

表 8 Bob探测器响应的可能情况

Table 8. Click probability of Bob’s detectors.

响应	$ {D_1}\left( {{t_0}} \right) $	$ {D_2}\left( {{t_0}} \right) $	$ {D_5}\left( {{t_1}} \right) $	$ {D_6}\left( {{t_1}} \right) $
概率	${1}/{4}$	${1}/{4}$	${1}/{4}$	${1}/{4}$

DownLoad: CSV

表 9 Eve制备的光子态及概率

Table 9. State and probability of photons prepared by Eve.

光子态	$ \left\| { + {t_0}} \right\rangle $	$ \left\| {H{t_ + }} \right\rangle $	$ \left\| {V{t_ - }} \right\rangle $
概率	${1}/{2}$	${1}/{4}$	${1}/{4}$

DownLoad: CSV

表 10 Eve制备的光子引起的探测器响应的可能情况

Table 10. Click and probability of detectors triggered by Eve’s photon.

探测器响应	$ {D_1}\left( {{t_0}} \right) $	$ {D_2}\left( {{t_0}} \right) $	$ {D_5}\left( {{t_1}} \right) $	$ {D_6}\left( {{t_1}} \right) $	$ {D_1}\left( {{t_1}} \right) $	$ {D_2}\left( {{t_1}} \right) $	$ {D_3}\left( {{t_1}} \right) $	$ {D_4}\left( {{t_1}} \right) $
概率	$ {3}/{{16}} $	$ {3}/{{16}} $	$ {3}/{{16}} $	$ {3}/{{16}} $	$ {1}/{{16}} $	$ {1}/{{16}} $	$ {1}/{{16}} $	$ {1}/{{16}} $

DownLoad: CSV

表 11 Bob探测器响应的可能情况

Table 11. Click probability of Bob’s detectors.

响应	$ {D_1}\left( {{t_1}} \right) $	$ {D_2}\left( {{t_1}} \right) $	$ {D_3}\left( {{t_1}} \right) $	$ {D_4}\left( {{t_1}} \right) $
概率	$1/{4}$	$1/{4}$	$1/{4}$	$1/{4}$

DownLoad: CSV

表 12 Eve制备的光子态及概率

Table 12. State and probability of photons prepared by Eve.

光子态	$ \left\| { - {t_1}} \right\rangle $	$ \left\| {H{t_ + }} \right\rangle $	$ \left\| {V{t_ - }} \right\rangle $
概率	$1/{2}$	$1/{4}$	$1/{4}$

DownLoad: CSV

表 13 Eve制备的光子引起的探测器响应的可能情况

Table 13. Click and probability of detectors triggered by Eve’s photon.

探测器响应	$ {D_1}\left( {{t_1}} \right) $	$ {D_2}\left( {{t_1}} \right) $	$ {D_3}\left( {{t_1}} \right) $	$ {D_4}\left( {{t_1}} \right) $	$ {D_1}\left( {{t_0}} \right) $	$ {D_2}\left( {{t_0}} \right) $	$ {D_5}\left( {{t_1}} \right) $	$ {D_6}\left( {{t_1}} \right) $
概率	$ {3}/{{16}} $	$ {3}/{{16}} $	$ {3}/{{16}} $	$ {3}/{{16}} $	$ {1}/{{16}} $	$ {1}/{{16}} $	$ {1}/{{16}} $	$ {1}/{{16}} $

DownLoad: CSV

map

[1]	Wehner S, Elkouss D, Hanso R 2018 Science 362 eaam9288 Google Scholar
[2]	Bennett C H, Brassard G 1984 Proceedings of the IEEE International Conference on Computers, Systems & Signal Processing Bangalore, India, December 10–12, 1984 p175
[3]	Ekert A K 1991 Phys. Rev. Lett. 67 661 Google Scholar
[4]	Bennett C H 1992 Phys. Rev. Lett. 68 3121 Google Scholar
[5]	Guo P L, Dong C, He Y, Jing F, He W T, Ren B C, Li C Y, Deng F G 2020 Opt. Express 28 4611 Google Scholar
[6]	Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145 Google Scholar
[7]	Long G L, Liu X S 2002 Phys. Rev. A 65 032302 Google Scholar
[8]	Deng F G, Long G L, Liu X S 2003 Phys. Rev. A 68 042317 Google Scholar
[9]	Deng F G, Long G L 2004 Phys. Rev. A 69 052319 Google Scholar
[10]	Wang C, Deng F G, Li Y S, Liu X S, Long G L 2005 Phys. Rev. A 71 044305 Google Scholar
[11]	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
[12]	Zhang W, Ding D S, Sheng Y B, Zhou L, Shi B S, Guo G C 2017 Phys. Rev. Lett. 118 220501 Google Scholar
[13]	Li T, Gao Z K, Li Z H 2020 EPL 131 60001 Google Scholar
[14]	Gao Z K, Li T, Li Z H 2019 EPL 125 40004 Google Scholar
[15]	Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1829 Google Scholar
[16]	Karlsson A, Koashi M, Imoto N 1999 Phys Rev. A 59 162 Google Scholar
[17]	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
[18]	Gao Z K, Li T, Li Z H 2020 Sci. Chin. -Phys. Mech. Astron. 63 120311 Google Scholar
[19]	Shimizu K, Imoto Y 1999 Phys. Rev. A 60 157 Google Scholar
[20]	Boström K, Felbinger T 2002 Phys. Rev. Lett. 89 187902 Google Scholar
[21]	Cai Q Y, Li B W 2004 Chin. Phys. Lett. 21 601 Google Scholar
[22]	Wójcik A 2003 Phys. Rev. Lett. 90 157901 Google Scholar
[23]	Long G L, Deng F G, Wang C, Li X H, Wen K, Wang W Y 2007 Front. Phys. Chin. 2 251
[24]	Li T, Long G L 2020 New J. Phys. 22 063017 Google Scholar
[25]	王明宇, 王馨德, 阮东, 龙桂鲁 2021 70 190301 Google Scholar Wang M Y, Wang X D, Ruan D, Long G L 2021 Acta Phys. Sin. 70 190301 Google Scholar
[26]	窦建鹏, 李航, 庞晓玲, 张超妮, 杨天怀, 金贤敏 2019 68 030307 Google Scholar Dou J P, Li H, Pang X L, Zhang C N, Yang T H, Jin X M 2019 Acta Phys. Sin. 68 030307 Google Scholar
[27]	Lucamarini M, Mancini S 2005 Phys. Rev. Lett. 94 140501 Google Scholar
[28]	Cai Q Y, Li B W 2004 Phys. Rev. A 69 054301 Google Scholar
[29]	Gao T, Yan F L, Wang Z X 2005 J. Phys. A:Gen. Phys. 38 5761 Google Scholar
[30]	Elsayed T A 2020 Phys. Scr. 96 025101 Google Scholar
[31]	Jeong Y C, Ji S W, Hong C, Park H S, Jang J 2020 Entropy 22 1268 Google Scholar
[32]	Jiang D, Chen Y, Gu X, Xie L, Chen L 2017 Sci. Rep. 7 44934 Google Scholar
[33]	Wang J D, Wei Z J, Zhang H, Qin X J, Liu X B, Zhang Z M, Liao C J, Liu S H 2010 J. Phys. B:At. Mol. Opt. Phys. 43 095504 Google Scholar
[34]	Lu H, Fung C, Ma X, Cai QY 2011 Phys. Rev. A 84 042344 Google Scholar
[35]	Beaudry N J, Lucamarini M, Mancini S, Renner R 2013 Phys. Rev. A 88 062302 Google Scholar
[36]	Henao C I, Serra R M 2015 Phys. Rev. A 92 052317 Google Scholar
[37]	Xu F, Ma X, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002 Google Scholar
[38]	Meyer-Scott E, Silberhorn C, Migdall A 2020 Rev. Sci. Instrum. 91 041101 Google Scholar
[39]	Kaneda F, Kwiat P G 2019 Sci. Adv. 5 eaaw8586 Google Scholar
[40]	Hall M A, Altepeter J B, Kumar P 2011 Phys. Rev. Lett. 106 053901 Google Scholar
[41]	Cao Y, Liang H, Yin J, Yong H L, Zhou F, Wu Y P, Ren J G, Li Y H, Pan G S, Yang T, Ma X, Peng C Z, Pan J W 2013 Opt. Express 21 27260 Google Scholar
[42]	Wang H, Li W, Jiang X, He Y M, Li Y H, Ding X, Chen M C, Qin J, Peng C Z, Schneider C, Kamp M, Zhang W J, Li H, You L X, Wang Z, Dowling J P, Höfling S, Lu C Y, Pan J W 2018 Phys. Rev. Lett. 120 230502 Google Scholar
[43]	Deng F G, Ren B C, Li X H 2017 Sci. Bull. 62 46 Google Scholar
[44]	Erhard M, Krenn M, Zeilinger A 2020 Nat. Rev. Phys. 2 365 Google Scholar
[45]	郭邦红, 杨理, 向憧, 关翀, 吴令安, 刘颂豪 2013 62 130303 Google Scholar Guo B H, Yang L, Xiang C, Guan C, Wu L A, Liu S H 2013 Acta Phys. Sin. 62 130303 Google Scholar

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Vol. 71, Issue 5 - 2022-03-05

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