1. R. Rivest, A. Shamir, and L. Adleman, “On Digital Signatures and Public-Key Cryptosystems,” MIT Laboratory for
Computer Science Technical Report TR-212 (1979).
2. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
3. G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key distribution scheme,” Phys. Rev. A
65(3), 032302 (2002).
4. F. G. Deng, G. L. Long, and X. S. Liu, “Two-step quantum direct communication protocol using the EinsteinPodolsky–Rosen pair block,” Phys. Rev. A 68(4), 042317 (2003).
Research Article
Vol. 29, No. 25 / 6 Dec 2021 / Optics Express 41532
5. W. Zhang, D. S. Ding, Y. B. Sheng, L. Zhou, B.-S. Shi, and G.-C. Guo, “Quantum secure direct communication with
quantum memory,” Phys. Rev. Lett. 118(22), 220501 (2017).
6. Z. Qi, Y. Li, Y. Huang, J. Feng, Y. Zheng, and X. Chen, “A 15-user quantum secure direct communication network,”
Light Sci Appl 10(1), 183 (2021).
7. A. Broadbent, J. Fitzsimons, and E. Kashefi, “Universal Blind Quantum Computation,” Proc. 50th Annu, IEEE Symp.
Found. Comput. Sci. (IEEE, 2009), pp. 517–526.
8. H.-J. Briegel, W. Dür, J. Cirac, and P. Zoller, “Quantum Repeaters: The Role of Imperfect Local Operations in
Quantum Communication,” Phys. Rev. Lett. 81(26), 5932–5935 (1998).
9. C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum Repeaters with Photon
Pair Sources and Multimode Memories,” Phys. Rev. Lett. 98(19), 190503 (2007).
10. C. Jones, D. Kim, M. Rakher, P. Kwiat, and T. Ladd, “Design and Analysis of Communication Protocols for Quantum
Repeater Networks,” New J. Phys. 18(8), 083015 (2016).
11. N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear
optics,” Rev. Mod. Phys. 83(1), 33–80 (2011).
12. L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles
and linear optics,” Nature 414(6862), 413–418 (2001).
13. N. Kalb, A. A. Reiserer, P. C. Humphreys, J. J. W. Bakermans, S. J. Kamerling, N. H. Nickerson, S. C. Benjamin, D.
J. Twitchen, M. Markham, and R. Hanson, “Entanglement distillation between solid-state quantum network nodes,”
Science 356(6341), 928–932 (2017).
14. B. K. Behera, S. Seth, A. Das, and P. K. Panigrahi, “Demonstration of entanglement purification and swapping
protocol to design quantum repeater in IBM quantum computer,” Quantum Inf Process 18(4), 108 (2019).
15. X.-M. Hu, C.-X. Huang, Y.-B. Sheng, L. Zhou, B.-H. Liu, Y. Guo, C. Zhang, W.-B. Xing, Y.-F. Huang, C.-F. Li,
and G.-C. Guo, “Long-Distance Entanglement Purification for Quantum Communication,” Phys. Rev. Lett. 126(1),
010503 (2021).
16. D. L-Rivera, S. Grandi, J. V. Rakonjac, A. Seri, and H. de Riedmatten, “Telecom-heralded entanglement between
multimode solid-state quantum memories,” Nature 594(7861), 37–40 (2021).
17. X. Liu, J. Hu, Z.-F. Li, X. Li, P.-Y. Li, P.-J. Liang, Z.-Q. Zhou, C.-F. Li, and G.-C. Guo, “Heralded entanglement
distribution between two absorptive quantum memories,” Nature 594(7861), 41–45 (2021).
18. M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory based on atomic frequency
combs,” Phys. Rev. A 79(5), 052329 (2009).
19. N. Sinclair, E. Saglamyurek, H. Mallahzadeh, J. A. Slater, M. George, R. Ricken, M. P. Hedges, D. Oblak, C. Simon,
W. Sohler, and W. Tittel, “Spectral Multiplexing for Scalable Quantum Photonics using an Atomic Frequency Comb
Quantum Memory and Feed-Forward Control,” Phys. Rev. Lett. 113(5), 053603 (2014).
20. D. Yoshida, K. Niizeki, S. Tamura, and T. Horikiri, “Entanglement distribution between quantum repeater nodes with
an absorptive type memory,” Int. J. Quantum Inf. 18(05), 2050026 (2020).
21. K. Niizeki, M. Zheng, X. Xie, K. Okamura, N. Takei, N. Namekata, S. Inoue, H. Kosaka, and T. Horikiri, “Ultrabright
narrow-band telecom two-photon source for long-distance quantum communication,” Appl. Phys. Exp. 11(4), 042801
(2018).
22. K. Niizeki, D. Yoshida, K. Ito, I. Nakamura, N. Takei, K. Okamura, M. Zheng, X. Xie, and T. Horikiri, “Two-photon
comb with wavelength conversion and 20-km distribution for quantum communication,” Commun. Phys. 3(1), 138
(2020).
23. M. Cristiani, H. de Riedmatten, J. Fekete, and D. Riela, “Ultranarrow-Band Photon-Pair Source Compatible with
Solid State Quantum Memories and Telecommunication Networks,” Phys. Rev. Lett. 110(22), 220502 (2013).
24. A. Amari, A. Walther, M. Sabooni, M. Huang, S. Kröll, M. Afzelius, I. Usmani, H. de Riedmatten, and N. Gisin,
“Towards an efficient atomic frequency comb quantum memory,” J,” Luminescence 130(9), 1579–1585 (2010).
25. P. Jobez, N. Timoney, C. Laplane, J. Etesse, A. Ferrier, P. Goldner, N. Gisin, and M. Afzelius, “Towards highly
multimode optical quantum memory for quantum repeaters,” Phys. Rev. A 93(3), 032327 (2016).
26. P. Jobez, I. Usmani, N. Timoney, C. Laplane, N. Gisin, and M. Afzelius, “Cavity-enhanced storage in an optical
spin-wave memory,” New J. Phys. 16(8), 083005 (2014).
27. Z.-Q. Zhou, J. Wang, C.-F. Li, and G.-C. Guo, “Efficient spectral hole-burning and atomic frequency comb storage in
Nd3+ :YLiF4 ,” Scien. Rep. 3(1), 2754 (2013).
28. M. Nilsson, L. Rippe, S. Kröll, R. Klieber, and D. Suter, “Hole burning techniques for isolation and study of individual
hyperfine transitions in inhomogeneously broadened solids demonstrated in Pr 3+ :Y2 SiO5 ,” Phys. Rev. B 70(21),
214116 (2004).
29. R. Equall, R. Cone, and R. Macfarlane, “Homogeneous broadening and hyperfine structure of optical transitions in
Pr3+ :Y2 SiO5 ,” Phys. Rev. B 52(6), 3963–3969 (1995).
30. M. Żukowski, A. Zeilinger, M. Horne, and A. Ekert, “‘‘Event-ready-detectors’’ Bell experiment via entanglement
swapping,” Phys. Rev. Lett. 71(26), 4287–4290 (1993).
31. L. Yu, C. Natarajan, T. Horikiri, C. Langrock, J. Pelc, M. Tanner, E. Abe, S. Maier, C. Schneider, S. Höfling, M. Kamp,
R. Hadfield, M. Fejer, and Y. Yamamoto, “Two-photon interference at telecom wavelengths for time-bin-encoded
single photons from quantum-dot spin qubits,” Nat. Commun. 6(1), 8955 (2015).
Research Article
Vol. 29, No. 25 / 6 Dec 2021 / Optics Express 41533
32. N. Sinclair, K. Heshami, C. Deshmukh, D. Oblak, C. Simon, and W. Tittel, “Proposal and proof-of-principle
demonstration of non-destructive detection of photonic qubits using a Tm:LiNbO3 waveguide,” Nat. Commun. 7(1),
13454 (2016).
33. M. Gündoğan, M. Mazzera, P. Ledingham, M. Cristiani, and H. de Riedmatten, “Coherent storage of temporally
multimode light using a spin-wave atomic frequency comb memory,” New J. Phys. 15(4), 045012 (2013).
34. N. Maring, K. Kutluer, J. Cohen, and M. Mazzera, “Storage of up-converted telecom photons in a doped crystal,”
New J. Phys. 16(11), 113021 (2014).
35. M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minář, H. de Riedmatten, N.
Gisin, and S. Kröll, “Demonstration of Atomic Frequency Comb Memory for Light with Spin-Wave Storage,” Phys.
Rev. Lett. 104(4), 040503 (2010).
36. N. Timoney, B. Lauritzen, I. Usmani, M. Afzelius, and N. Gisin, “Atomic frequency comb memory with spin-wave
storage in 153 Eu3 + :Y2 SiO5 ,” J. Phys. B: At. Mol. Opt. Phys. 45(12), 124001 (2012).
37. T. Miyashita, T. Kondo, K. Ikeda, K. Yoshii, F. -L. Hong, and T. Horikiri, “Offset-locking-based frequency stabilization
of external cavity diode lasers for long-distance quantum communication,” arXiv:2108.13130 [quant-ph] (2021).
38. Y. Hisai, K. Ikeda, H. Sakagami, T. Horikiri, T. Kobayashi, K. Yoshii, and F.-L. Hong, “Evaluation of laser frequency
offset locking using an electrical delay line,” Appl. Opt. 57(20), 5628–5634 (2018).
39. P. W. Milonni, “Controlling the speed of light pulses,” J. Phys. B: At. Mol. Opt. Phys. 35(6), R31–R56 (2002).
40. M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Experimental superradiance and slow-light effects for
quantum memories,” Phys. Rev. A 80(1), 012317 (2009).
41. Y. Asahina, K. Yoshii, Y. Yamada, Y. Hisai, S. Okubo, M. Wada, H. Inaba, T. Hasegawa, Y. Yamamoto, and F.-L.
Hong, “Narrow-linewidth and highly stable optical frequency comb realized with a simple electro-optic modulator
system in a mode-locked Er:fiber laser,” Jpn. J. Appl. Phys. 58(3), 038003 (2019).
42. F.-L. Hong and J. Ishikawa, “Hyperfine structures of the R(122)35-0 and P(84)33-0 transitions of 127 I2 near 532 nm,”
Optics Commun. 183(1-4), 101–108 (2000).
43. M. Nicolle, J. N. Becker, C. Weinzetl, I. A. Walmsley, and P. M. Ledingham, “Gigahertz-bandwidth optical memory
in Pr3+ :Y2 SiO5 ,” Opt. Lett. 46(12), 2948–2951 (2021).
44. A. Seri, D. L. Rivera, A. Lenhard, G. Corrielli, R. Osellame, M. Mazzera, and H. de Riedmatten, “Quantum Storage
of Frequency-Multiplexed Heralded Single Photons,” Phys. Rev. Lett. 123(8), 080502 (2019).
45. C. W. Thiel, R. M. Macfarlane, Y. Sun, T. Böttger, N. Sinclair, W. Tittel, and R. L. Cone, “Measuring and analyzing
excitation-induced decoherence in rare-earth-doped optical materials,” Laser Phys. 24(10), 106002 (2014).
46. B. S. Ham and P. R. Hemmer, “Population shelved all-optical modulation,” Phys. Rev. B 68(7), 073102 (2003).
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