• Chinese Optics Letters
  • Vol. 21, Issue 4, 042702 (2023)
Huicun Yu1、2, Bangying Tang3, Jiahao Li1, Yuexiang Cao1, Han Zhou3, Sichen Li3, Haoxi Xiong4, Bo Liu2、*, and Lei Shi1、**
Author Affiliations
  • 1Information and Navigation College, Air Force Engineering University, Xi’an 710077, China
  • 2College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China
  • 3College of Computer and Science, National University of Defense Technology, Changsha 410073, China
  • 4Teaching and Research Support Center, National University of Defense Technology, Changsha 410073, China
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    DOI: 10.3788/COL202321.042702 Cite this Article Set citation alerts
    Huicun Yu, Bangying Tang, Jiahao Li, Yuexiang Cao, Han Zhou, Sichen Li, Haoxi Xiong, Bo Liu, Lei Shi. Satellite-to-aircraft quantum key distribution performance estimation with boundary layer effects[J]. Chinese Optics Letters, 2023, 21(4): 042702 Copy Citation Text show less

    Abstract

    Remarkable progress has been made in satellite-based quantum key distribution (QKD), which can effectively provide QKD service even at the intercontinental scale and construct an ultralong-distance global quantum network. But there are still some places where terrestrial fiber and ground stations cannot be constructed, like harsh mountainous areas and air space above the sea. So the airborne platform is expected to replace the ground station and provide flexible and relay links for the large-scale integrated communication network. However, the photon transmission rate would be randomly reduced, owing to the randomly distributed boundary layer that surrounds the surface of the aircraft when the flight speed is larger than 0.3 Ma. Previous research of airborne QKD with boundary layer effects is mainly under the air-to-ground scenario in which the aircraft is a transmitter, while the satellite-to-aircraft scenario is rarely reported. In this article, we propose a performance evaluation scheme of satellite-to-aircraft QKD with boundary layer effects in which the aircraft is the receiver. With common experimental settings, the boundary layer would introduce a 31 dB loss to the transmitted photons, decrease 47% of the quantum communication time, and decrease 51% of the secure key rate, which shows that the aero-optical effects caused by the boundary layer cannot be ignored. Our study can be performed in future airborne quantum communication designs.
    α=arctan[sin(|lAlB|)cos(LA)cos(LB)sin(LA)cos(LA)sin(LB)cos(LBLA)],

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    d=(r+hA)[1+(r+hBr+hA)22(r+hBr+hA)cos(γ)]1/2,

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    cos(γ)=cos(LB)cos(LA)cos(lAlB)+sin(LB)sin(LA),

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    β=arccos[(r+hA)sin(γ)d].

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    n=1+ρKGD,

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    KGD=2.23×104×(1+7.52×103λ2).

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    ddp(ndsdp)=n,

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    {dFdp=ndsdp=1nF,

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    s=(xyz),F=(FxFyFz)=n(dxdpdydpdzdp).

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    OPL(x,y,t)=Pn(x,y,t)dp.

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    OPD(x,y,t)=OPL(x,y,t)OPL¯.

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    ϕ=2π·OPDλ.

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    ωDP=ωD2+(σT·d)2,

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    ωD=dλπ·ω0[1+0.83sinβ(DTr0)5/3]3/5,

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    s0=[x1y1z1x2y2z2xmymzm],

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    F0=n(cosαcosβsinαcosβsinβ),

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    {rn+1=rn+16h{Tn+2[Tn+h2D(rn)]+2[Tn+h2D(rn+h2Tn)]}+16h{Tn+hD[rn+h2Tn+h24D(rn)]}Tn+1=Tn+16h{2D(rn+h2Tn)+2D[rn+h2Tn+h24D(rn)]}+16h{D(rn)+D[rn+hTn+h22D(rn)]},

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    D=n(nxnynz).

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    η0=SR·exp(τsinβ)·{1exp[0.5(DRωDP)2]},

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    SRexp(ϕrms2).

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    η=η0ηsηd,

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    Rq{Q1[1H2(e1)]Qµf(Eµ)H2(Eµ)},

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    H2(x)=xlog(x)(1x)log(1x).

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    Qµ=Y0+1eηµ,

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    EµQµ=e0Y0+ed(1eηµ),

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    Eµ=EµQµ/Qµ.

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    Q1Q1L,ν,0=µ2eµµνν2(QνeνQµeµν2µ2µ2ν2µ2Y0),

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    e1e1U,ν,0=EνQνeνe0Y0Y1L,ν,0ν,

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    Y1L,ν,0=Q1µeµ.

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    EνQν=e0Y0+ed(1eην).

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    Huicun Yu, Bangying Tang, Jiahao Li, Yuexiang Cao, Han Zhou, Sichen Li, Haoxi Xiong, Bo Liu, Lei Shi. Satellite-to-aircraft quantum key distribution performance estimation with boundary layer effects[J]. Chinese Optics Letters, 2023, 21(4): 042702
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