• Chinese Optics Letters
  • Vol. 20, Issue 9, 092701 (2022)
Jipeng Wang, Zhenhua Li, Zhongqi Sun, Tianqi Dou, Wenxiu Qu, Fen Zhou, Yanxin Han, Yuqing Huang, and Haiqiang Ma*
Author Affiliations
  • School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China
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    DOI: 10.3788/COL202220.092701 Cite this Article
    Jipeng Wang, Zhenhua Li, Zhongqi Sun, Tianqi Dou, Wenxiu Qu, Fen Zhou, Yanxin Han, Yuqing Huang, Haiqiang Ma. Loss-tolerant measurement device independent quantum key distribution with reference frame misalignment[J]. Chinese Optics Letters, 2022, 20(9): 092701 Copy Citation Text show less

    Abstract

    Reference frame independent and measurement device independent quantum key distribution (RFI-MDI-QKD) has the advantages of being immune to detector side loopholes and misalignment of the reference frame. However, several former related research works are based on the unrealistic assumption of perfect source preparation. In this paper, we merge a loss-tolerant method into RFI-MDI-QKD to consider source flaws into key rate estimation and compare it with quantum coin method. Based on a reliable experimental scheme, the joint influence of both source flaws and reference frame misalignment is discussed with consideration of the finite-key effect. The results show that the loss-tolerant RFI-MDI-QKD protocol can reach longer key rate performance while considering the existence of source flaws in a real-world implementation.
    Qiα,jβMaMb,U=Qiα,jβMaMb(1+ξlr),Qiα,jβMaMb,L=Qiα,jβMaMb(1ξlr),f(ϵ1.5)NMaMbQiα,jβMaMbξMaMbf(ϵ4/16)NMaMbQiα,jβMaMb.

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    Yiα,jβL=μa2μbS1va2vbS2μaμbvavb(μava),S1=Qiα,jβvaνb,Le(νa+νb)+Qiα,jβ0a0b,LQiα,jβva0b,UevaQiα,jβ0avb,Uevb,S2=Qiα,jβμaμb,Ue(μa+μb)+Qiα,jβ0a0b,UQiα,jβμa0b,LeμaQiα,jβ0aμb,Leμb,Yiα,jβU=e(va+vb)Qiα,jβ0a0b,U+Qiα,jβvavb,UevaQiα,jβva0b,LevbQiα,jβ0abb,Lνavb.

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    RL=μaμbe(μa+μb)(1IE)α=β=ZYiα,jβLλEC,IE=(1EZZ11,U)h(1+vmax2)+EZZ11,Uh[1+f(vmax)2],f(vmax)=CL2(1EZZ11,U)2vmax2EZZ11,U,vmax=min(11EZZ11,UCL2,1).

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    CL=α,β{X,Y}min:(12Eαβ11)2,s.t.Eαβ11,LEαβ11Eαβ11,U.

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    |ΨA=12(|0ZA1|ϕ0ZA2E+|1ZA1|ϕ1ZA2E),

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    |ΨA=12(|0XA1|ϕ0XvirA2E+|1XA1|ϕ1XvirA2E),|ΨA=12(|0YA1|ϕ0YvirA2E+|1YA1|ϕ1YvirA2E).

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    Yiα,jβvir=PiαvirPjβvir[SσtAiα,vir(SσtBjβ,vir)T]·qσtAσtB,

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    SσtAiα,vir=[SIAiα,vir,SXAiα,vir,SYAiα,vir,SZAiα,vir],SσtBjβ,vir=[SIBjβ,vir,SXBjβ,vir,SYBjβ,vir,SZBjβ,vir],qσtAσtB=[qIAIB,qIAXB,qIAYB,qIAZB,qXAIB,qXAXB,qXAYB,qXAZB,qYAIB,qYAXB,qYAYB,qYAZB,qZAIB,qZAXB,qZAYB,qZAZB].

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    qσtAσtB=Yiα,jβPiαPjβ[SσtAiα(SσtBjβ)T].

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    |ϕ0ZA=|0Z,|ϕ1ZA=|1Z,|ϕ0XA=|0Z+|1Z2=|0X,|ϕ0YA=|0Z+i|1Z2=|0Y,

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    |ϕ0ZB=cos(δ1)|0Z+sin(δ1)|1Z,|ϕ1ZB=sin(δ2)|0Z+cos(δ2)|1Z,|ϕ0XB=sin(π4+δ3)|0Z+cos(π4+δ3)ei(θ1+ω)|1Z,|ϕ0YB=sin(π4+δ3)|0Z+cos(π4+δ3)ei(π2+θ2+ω)|1Z.

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    Q0=12π02π1(1edark)exp(|A+eiΔϕB|2)dΔϕ,Q1=12π02π1(1edark)exp(|A+eiπeiΔϕB|2)dΔϕ,

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    Jipeng Wang, Zhenhua Li, Zhongqi Sun, Tianqi Dou, Wenxiu Qu, Fen Zhou, Yanxin Han, Yuqing Huang, Haiqiang Ma. Loss-tolerant measurement device independent quantum key distribution with reference frame misalignment[J]. Chinese Optics Letters, 2022, 20(9): 092701
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