我的實驗主要分成兩部分：首先我們將波長為1550nm的雷射衰減至平均光子數約為0.1顆來模擬單光子光源，利用這個方法來初步測試差分移相量子密鑰分發的工作原理，並且利用長光纖測試遠距離傳輸的可行性；之後利用775nm的雷射當作入射光打入特殊設計的非線性晶體內，透過非線性效應產生一對1550nm的窄頻雙光子，藉此來實現以單光子為光源的差分移相量子密鑰分發。以衰減雷射當光源時，我們的錯誤率均小於2%，每秒可以產生2k個密鑰，而且我們的傳輸距離在實驗室內可以達到25km。而以單光子為光源實現差分移相量子密鑰分發的部分，我們測得的錯誤率約為5%，密鑰產生效率高於90%，而每秒可以產生約20個密鑰。透過這種作法，我們初步實現利用通訊波段的單光子進行差分移相量子密鑰分發。

In this thesis, my experiment can be divided into two parts. Firstly, we simulate a single photon source by attenuated 1550nm laser with average number of photons of 0.1. We use this source to test whether we can implement the differential phase shift quantum key distribution or not. Then, we use long fiber to test the long distance quantum key distribution. Secondly, we use 775nm laser to pump the nonlinear crystal which has special design. By nonlinear effect, we can create narrowband bi-photon whose wavelengths are 1550nm. Using this as signal source, we implement the differential phase shift quantum distribution. When we use attenuated laser as sources, our key rate is about 2000 per second and the error rate is below 2%. Moreover, our experiment shows that the transmission distance can reach 25km. And, when we use single photons as sources, our key rate is about 20 per second, the error rate is about 5% and the key creation efficiency is above 90%. This work shows the first step of using telecom band single-photon source to implement differential phase shift quantum key distribution.

第一章 實驗目的與研究方法 5
第二章 文獻回顧 6
第三章 實驗原理 8
3.1 DPS-QKD 8
3.1.1. 原理介紹 8
3.1.2. 密鑰生成效率 10
3.1.3. 密鑰安全問題 12
3.2 單光子光源 19
3.2.1. 原理介紹 19
3.2.2. 光源與密鑰產生率 22
第四章 實驗架設及量測方法 25
4.1 DPS-QKD 實驗架設 25
4.1.1. 光路架設 25
4.1.2. Vπ測量與優化 28
4.1.3. 干涉儀穩定性測量 31
4.1.4. EOM優化與Vπ測試 34
4.1.5. DPS系統測試 36
4.2 單光子光源 39
4.2.1. 光路架設 39
4.2.2. 系統優化 41
4.2.3. 穩定波長機制 42
4.2.4. 光參量震盪器（Optical Parametric Oscillator, OPO） 44
第五章 結果討論 47
5.1 帕松分布測量 47
5.2 類單光子光源DPS-QKD 52
5.2.1. 三個脈衝 52
5.2.2. 密鑰生成與即時更新 55
5.2.3. 長距離傳輸結果 58
5.3 單光子光源 59
5.3.1. 光參數震盪器 59
5.3.2. 光子G2(τ)圖 61
5.3.3. 三重反關聯參數測量 62
5.3.4. 波形調製 63
5.3.5. 單光子光源三個脈衝 64
5.3.6. 脈衝數與密鑰產生率 66
第六章 總結與未來展望 70
附錄A 光束分裂攻擊 71
附錄B 帕松分布修正 72
參考文獻 73

1. Ducklin, P. Belgian programmer solves cryptographic puzzle-15 years too soon! 2019; Available from: https://nakedsecurity.sophos.com/2019/05/03/belgian-programmer-solves-cryptographic-puzzle-15-years-too-soon/.
2. Shor, P.W. Algorithms for quantum computation: Discrete logarithms and factoring. in Proceedings 35th annual symposium on foundations of computer science. 1994. Ieee.
3. Inoue, K., E. Waks, and Y. Yamamoto, Differential phase shift quantum key distribution. Physical review letters, 2002. 89(3): p. 037902.
4. Wiesner, S., Conjugate coding. ACM Sigact News, 1983. 15(1): p. 78-88.
5. Bennett, C.H. and G. Brassard, Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing. 1984, IEEE New York.
6. Bennett, C.H., G. Brassard, and N.D. Mermin, Quantum cryptography without Bell’s theorem. Physical Review Letters, 1992. 68(5): p. 557.
7. Ekert, A.K., Quantum cryptography based on Bell’s theorem. Physical review letters, 1991. 67(6): p. 661.
8. Bennett, C.H., Quantum cryptography using any two nonorthogonal states. Phys Rev Lett, 1992. 68(21): p. 3121-3124.
9. Stucki, D., et al., Fast and simple one-way quantum key distribution. Applied Physics Letters, 2005. 87(19): p. 194108.
10. Liao, S.-K., et al., Satellite-to-ground quantum key distribution. Nature, 2017. 549(7670): p. 43.
11. Bouchard, F., et al., Underwater quantum key distribution in outdoor conditions with twisted photons. arXiv preprint arXiv:1801.10299, 2018.
12. Hwang, W.-Y., Quantum key distribution with high loss: toward global secure communication. Physical Review Letters, 2003. 91(5): p. 057901.
13. Hillery, M., Quantum cryptography with squeezed states. Physical Review A, 2000. 61(2): p. 022309.
14. Cerf, N.J., M. Levy, and G. Van Assche, Quantum distribution of Gaussian keys using squeezed states. Physical Review A, 2001. 63(5): p. 052311.
15. Ralph, T.C., Continuous variable quantum cryptography. Physical Review A, 1999. 61(1): p. 010303.
16. Huang, D., et al., Long-distance continuous-variable quantum key distribution by controlling excess noise. Scientific reports, 2016. 6: p. 19201.
17. Zhang, Y., et al., Continuous-variable QKD over 50 km commercial fiber. Quantum Science and Technology, 2019. 4(3): p. 035006.
18. Stucki, D., et al., High rate, long-distance quantum key distribution over 250 km of ultra low loss fibres. New Journal of Physics, 2009. 11(7): p. 075003.
19. Shimizu, K., et al., Performance of long-distance quantum key distribution over 90-km optical links installed in a field environment of Tokyo metropolitan area. Journal of Lightwave Technology, 2013. 32(1): p. 141-151.
20. Liu, C., et al., Differential-phase-shift quantum key distribution using heralded narrow-band single photons. Opt Express, 2013. 21(8): p. 9505-13.
21. Bennett, C.H., et al., Generalized privacy amplification. IEEE Transactions on Information Theory, 1995. 41(6): p. 1915-1923.
22. Yan, H., S.-L. Zhu, and S.-W. Du, Efficient Phase-Encoding Quantum Key Generation with Narrow-Band Single Photons. Chinese Physics Letters, 2011. 28(7).
23. Wootters, W.K. and W.H. Zurek, A single quantum cannot be cloned. Nature, 1982. 299(5886): p. 802.
24. Inoue, K., Differential Phase-Shift Quantum Key Distribution Systems. IEEE Journal of Selected Topics in Quantum Electronics, 2015. 21(3): p. 109-115.
25. Inoue, K. and T. Honjo, Robustness of differential-phase-shift quantum key distribution against photon-number-splitting attack. Physical Review A, 2005. 71(4).
26. Curty, M., et al., Sequential attacks against differential-phase-shift quantum key distribution with weak coherent states. arXiv preprint quant-ph/0609094, 2006.
27. Honjo, T., et al., Countermeasure against tailored bright illumination attack for DPS-QKD. Optics Express, 2013. 21(3): p. 2667-2673.
28. Lydersen, L., J. Skaar, and V. Makarov, Tailored bright illumination attack on distributed-phase-reference protocols. Journal of Modern Optics, 2011. 58(8): p. 680-685.
29. Waks, E., H. Takesue, and Y. Yamamoto, Security of differential-phase-shift quantum key distribution against individual attacks. Physical Review A, 2006. 73(1).
30. Wen, K., K. Tamaki, and Y. Yamamoto, Unconditional security of single-photon differential phase shift quantum key distribution. Phys Rev Lett, 2009. 103(17): p. 170503.
31. Shor, P.W. and J. Preskill, Simple proof of security of the BB84 quantum key distribution protocol. Physical review letters, 2000. 85(2): p. 441.
32. Boyd, R.W., Nonlinear Optics, Third Edition. 2008: Academic Press, Inc. 640.
33. Chuu, C.-S., G.Y. Yin, and S.E. Harris, A miniature ultrabright source of temporally long, narrowband biphotons. Applied Physics Letters, 2012. 101(5): p. 051108.
34. Fradkin, K., et al., Tunable midinfrared source by difference frequency generation in bulk periodically poled KTiOPO 4. Applied physics letters, 1999. 74(7): p. 914-916.
35. König, F. and F.N. Wong, Extended phase matching of second-harmonic generation in periodically poled KTiOPO 4 with zero group-velocity mismatch. Applied physics letters, 2004. 84(10): p. 1644-1646.
36. Honjo, T., T. Inoue, and K. Inoue, Influence of light source linewidth in differential-phase-shift quantum key distribution systems. Optics Communications, 2011. 284(24): p. 5856-5859.
37. Honjo, T., K. Inoue, and H. Takahashi, Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach–Zehnder interferometer. Optics letters, 2004. 29(23): p. 2797-2799.