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Security of continuous-variable quantum key distribution with four-state protocol based on discrete modulation of noisy coherent states is analyzed. Combing discrete modulation and reverse reconciliation, this protocol can be used for long distance cryptography. There is a small difference between the state Alice sends in the discrete modulation protocol and the Gaussian modulation protocol, and it can be treated as excess noise and loss in the channel. As Alice cannot do a precise modulation, she will induce noise to the coherent state. We look this noise as the source noise and derive a lower bound to the secure key rate assuming the eavesdropper cannot benefit from the noise in the source. For avoiding the fast and random phase locking between the signal and local oscillator in experiment, we also analyze the security of four-state protocol using no-switching scheme.
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Keywords:
- discrete modulation /
- the four-state protocol /
- continuous variable quantum key distribution /
- secure key rate
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[2] ［2]Weedbrook C, Lance A M , Bowen W P, Symul T, Ralph T C, Lam P K 2004 Phys. Rev. Lett. 93 170504
[3] ［3]Grosshans F, Van Assche G, Wenger J, Tualle-Brouri R, Cerf N J, Grangier P 2003 Nature 421 238
[4] ［4]Lance A M, Symul T, Sharma V, Weedbrook C, Ralph T C, Lam P K 2005 Phys. Rev. Lett. 95 180503
[5] ［5]Lodewyck J, Bloch M, García-Patrón R, Fossier S, Karpov E, Diamanti E, Debuisschert T, Cerf N J, Tualle-Brouri R,
[6] McLaughlin S W, Grangier P 2007 Phys. Rev. A 76 042305
[7] ［6]Qi B, Huang L L, Qian L, Lo H K 2007 Phys. Rev. A 76 052323
[8] ［7]Zhu C H, Pei C X, Quan D X, Chen N, Yi Y H 2009 Acta Phys. Sin. 58 2184 （in Chinese）［朱畅华、裴昌幸、权东晓、陈南、易运晖 2009 58 2184］
[9] ［8]Lodewyck J, Debuisschert T, Tualle-Brouri R, Grangier P 2005 Phys. Rev. A 72 050303
[10] ［9]Chen J J, Hua Z F, Zhao Y B, Gui Y Z, Guo G C 2007 Acta Phys. Sin. 56 5 （in Chinese）［陈进建、 韩正甫、赵义博、桂有珍、郭光灿 2007 56 5］
[11] ［10]Leverrier A, Grangier P 2009 Phys. Rev. Lett. 102 180504
[12] ［11]Renner R, Cirac J I 2009 Phys. Rev. Lett. 102 110504
[13] ［12]Leverrier A, Karpov E, Grangier P, Cerf N J www.arxiv.org/pdf/quant-ph/08092252
[14] ［13]Renner R, Knig R www.arxiv.org/pdf/quant-ph/0403133
[15] ［14]Bloch M, Thangaraj A, McLaughlin S W www.arxiv.org/pdf/cs.IT/0509041
[16] ［15]Leverrier A, Alléaume R, Boutros J, Zémor G, Grangier P 2008 Phys. Rev. A 77 042325
[17] ［16]Grosshans F, Cerf N J 2003 Quantum Inf. Comput. 3 535
[18] ［17]Shen Y, Yang J, Guo H 2009 J.Phys. B 42 235506
[19] ［18]Serafini A, Illuminati F, De Siena S 2004 J. Phys. B 37 L21
[20] ［19]García-Patrón R, Cerf N J 2006 Phys. Rev. Lett. 97 190503
[21] ［20]Scarani V, Pasquinucci H B, Cerf N J, Duek M, Lütkenhaus N, Peev M 2009 Rev.Mod.Phys. 81 1301
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[1] ［1]Grosshans F, Grangier P 2002 Phys. Rev. Lett. 88 057902
[2] ［2]Weedbrook C, Lance A M , Bowen W P, Symul T, Ralph T C, Lam P K 2004 Phys. Rev. Lett. 93 170504
[3] ［3]Grosshans F, Van Assche G, Wenger J, Tualle-Brouri R, Cerf N J, Grangier P 2003 Nature 421 238
[4] ［4]Lance A M, Symul T, Sharma V, Weedbrook C, Ralph T C, Lam P K 2005 Phys. Rev. Lett. 95 180503
[5] ［5]Lodewyck J, Bloch M, García-Patrón R, Fossier S, Karpov E, Diamanti E, Debuisschert T, Cerf N J, Tualle-Brouri R,
[6] McLaughlin S W, Grangier P 2007 Phys. Rev. A 76 042305
[7] ［6]Qi B, Huang L L, Qian L, Lo H K 2007 Phys. Rev. A 76 052323
[8] ［7]Zhu C H, Pei C X, Quan D X, Chen N, Yi Y H 2009 Acta Phys. Sin. 58 2184 （in Chinese）［朱畅华、裴昌幸、权东晓、陈南、易运晖 2009 58 2184］
[9] ［8]Lodewyck J, Debuisschert T, Tualle-Brouri R, Grangier P 2005 Phys. Rev. A 72 050303
[10] ［9]Chen J J, Hua Z F, Zhao Y B, Gui Y Z, Guo G C 2007 Acta Phys. Sin. 56 5 （in Chinese）［陈进建、 韩正甫、赵义博、桂有珍、郭光灿 2007 56 5］
[11] ［10]Leverrier A, Grangier P 2009 Phys. Rev. Lett. 102 180504
[12] ［11]Renner R, Cirac J I 2009 Phys. Rev. Lett. 102 110504
[13] ［12]Leverrier A, Karpov E, Grangier P, Cerf N J www.arxiv.org/pdf/quant-ph/08092252
[14] ［13]Renner R, Knig R www.arxiv.org/pdf/quant-ph/0403133
[15] ［14]Bloch M, Thangaraj A, McLaughlin S W www.arxiv.org/pdf/cs.IT/0509041
[16] ［15]Leverrier A, Alléaume R, Boutros J, Zémor G, Grangier P 2008 Phys. Rev. A 77 042325
[17] ［16]Grosshans F, Cerf N J 2003 Quantum Inf. Comput. 3 535
[18] ［17]Shen Y, Yang J, Guo H 2009 J.Phys. B 42 235506
[19] ［18]Serafini A, Illuminati F, De Siena S 2004 J. Phys. B 37 L21
[20] ［19]García-Patrón R, Cerf N J 2006 Phys. Rev. Lett. 97 190503
[21] ［20]Scarani V, Pasquinucci H B, Cerf N J, Duek M, Lütkenhaus N, Peev M 2009 Rev.Mod.Phys. 81 1301
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