• Infrared and Laser Engineering
  • Vol. 50, Issue 11, 20210124 (2021)
Tianxiu Li, Lei Shi, Jiahao Li, and Junhui Wang
Author Affiliations
  • College of Information and Navigation, Air Force Engineering University, Xi’an 710077, China
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    DOI: 10.3788/IRLA20210124 Cite this Article
    Tianxiu Li, Lei Shi, Jiahao Li, Junhui Wang. Performance of Measurement Device Independent Quantum Key Distribution on flight repeater platform[J]. Infrared and Laser Engineering, 2021, 50(11): 20210124 Copy Citation Text show less

    Abstract

    Quantum Key Distribution (QKD) technology now is used in more fields with its good security and confidentiality performance can effectively deal with communication security threats. The application of QKD technology based on aviation flight platform is expected to greatly improve the security level of aviation communication system and provide reliable guarantee for local area secure communication. To analyze airborne application of Measurement Device Independent QKD(MDI-QKD) with asymmetric transmission efficiency, the simulation analysis model combined with the decoy state method was established. The effect of meteorological conditions, flight height on the performance of the system simulation were analyzed. The results show that the application of MDI-QKD protocol in the air mobile platform at the common flight altitude of early-warning aircraft can provide combat communication guarantee under the fine weather with the visibility of about 15 km, but there are communication blind areas and movement restrictions of the flight platform in the long-distance communication. Further experiment indicates the adjustment of signal pulse intensity is an effective method to improve the performance. Above all, the experiment provides theoretical basis and optimization method for the further research and practical application of QKD on flight repeater platform.
    $\begin{gathered} {{R}} \geqslant {\mu _{\rm{2}}}{\nu _{\rm{2}}}{\rm{exp}}\left( { - {\mu _{\rm{2}}} - {\nu _{\rm{2}}}} \right)Y_{11}^Z\left[ {1 - H\left( {e_{11}^x} \right)} \right] {\rm{ }} - Q_{{\mu _{\rm{2}}}{\nu _{\rm{2}}}}^{\textit{z}}{f_{}}H\left( {E_{{\mu _{\rm{2}}}{\nu _{\rm{2}}}}^{\textit{z}}} \right) \\ \end{gathered} $(1)

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    $\begin{gathered} Y_{11}^\omega \geqslant \frac{{g_1^\omega + g_2^\omega + g_3^\omega - \exp \left( {{\mu _2} + {\nu _2}} \right)Q_{{\mu _2}{\nu _2}}^\omega }}{{{\mu _1}{\nu _1} - {\mu _2}{\nu _2} + \alpha {\mu _2}{\nu _1} \alpha {\mu _1}{\nu _2}}} + \\ \frac{{\exp \left( {{\mu _1} + {\nu _1}} \right)Q_{{\mu _1}{\nu _1}}^\omega }}{{{\mu _1}{\nu _1} - {\mu _2}{\nu _2} + \alpha {\mu _2}{\nu _1} + \alpha {\mu _1}{\nu _2}}} \\ \end{gathered} $(2)

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    $e_{11}^\omega \leqslant \frac{{\exp \left( {{\mu _1} + {\nu _1}} \right)Q_{{\mu _1}{\nu _1}}^\omega E_{{\mu _1}{\nu _1}}^\omega - g_4^\omega }}{{{\mu _1}{\nu _1}Y_{11}^\omega }}$(3)

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    $Q_{{\mu _i}{\nu _j}}^x = 2{y^2}\left[ {1 + 2{y^2} - 4y{I_0}\left( s \right) + {I_0}\left( {2s} \right)} \right]$(4)

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    $Q_{{\mu _i}{\nu _j}}^xE_{{\mu _i}{\nu _j}}^x = {e_0}Q_{{\mu _i}{\nu _j}}^x - 2\left( {{e_0} - {e_d}} \right){y^2}\left[ {{I_0}\left( {2s} \right) - 1} \right]$(5)

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    $Q_{{\mu _i}{\nu _j}}^z = {Q_c} + {Q_E}$(6)

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    $Q_{{\mu _i}{\nu _j}}^zE_{{\mu _i}{\nu _j}}^z = {e_d}{Q_c} + \left( {1 - {e_d}} \right){Q_E}$(7)

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    $s = \frac{{\sqrt {{\eta _a}{\mu _i}{\eta _b}{\nu _j}} }}{2}$(8)

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    $y = \left( {1 - {P_d}} \right)\exp \left( { - \frac{{\mu '}}{4}} \right)$(9)

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    $\mu ' = {\eta _a}{\mu _i} + {\eta _b}{\nu _j}$(10)

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    $\eta {\rm{ = }}{\eta _{{\rm{atm}}}} \times {\eta _D} \times {\eta _{diff}}$(11)

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    ${\eta _{{\rm{atm}}}} = {\eta _{\rm abs}}{\eta _{\rm turb}}$(12)

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    ${\eta _{{\rm{abs}}}} = \exp \left( { - \alpha L} \right)$(13)

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    ${\eta _{\rm turb}} = \dfrac{{{{\left( {\dfrac{\lambda }{{{R_t}}}} \right)}^2}}}{{{{\left( {\dfrac{\lambda }{{{R_t}}}} \right)}^2} + \theta _{\rm turb}^2}}$(14)

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    $\begin{array}{l} {L_{AC}} = \dfrac{h}{{{\rm{cos}}\left[ {\arctan \left( {\dfrac{{{l_A}}}{h}} \right)} \right]}} \\{L_{BC}} = \dfrac{h}{{{\rm{cos}}\left[ {\arctan \left( {\dfrac{{{l_B}}}{h}} \right)} \right]}}\end{array} $(15)

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    $\alpha \left( \lambda \right){\rm{ = }}\left( {\frac{{{\rm{3}}{\rm{.91}}}}{{{V_v}}}} \right){\left( {\frac{{0.55}}{\gamma }} \right)^q}$(16)

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    $q = \left\{ {\begin{array}{*{20}{c}} {1.6,{\rm{ }}\;{V_v} > 50{\rm{ }}\;{\rm{km}}{\rm{ }}} \\ {1.3,{\rm{ }}6{\rm{ }}\;{\rm{km}} < {V_v} < 50{\rm{ }}\;{\rm{km}}{\rm{ }}} \\ {0.16{\rm{ }}{V_v} + 0.34,{\rm{ }}1{\rm{ }}\;{\rm{km}} < {V_v} < 6{\rm{ }}\;{\rm{km}}} \\ {{V_v} - 0.5,{\rm{ }}0.5{\rm{ }}\;{\rm{km}} < {V_v} < 1{\rm{ }}\;{\rm{km}}{\rm{ }}} \\ {0,{\rm{ }}{V_v} < 0.5{\rm{ }}\;{\rm{km}}{\rm{ }}} \end{array}} \right.$(17)

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    ${\eta _{diff}} = \left( {{{\rm e}^{ - 2\gamma _t^2\alpha _t^2}} - {{\rm e}^{ - 2\alpha _t^2}}} \right)\left( {{{\rm e}^{ - 2\gamma _r^2\alpha _r^2}} - {{\rm e}^{ - 2\alpha _r^2}}} \right)$(18)

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    $ \gamma _{t,r}^{} = \frac{{{b_{t,r}}}}{{{R_{t,r}}}},\alpha _{t,r}^{} = \frac{{{R_{t,r}}}}{{{\omega _{t,r}}}},{\omega _t} = {R_t},{\omega _r} = \frac{{\sqrt 2 \lambda L}}{{\pi {R_t}}} $(19)

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    $\begin{array}{l} Q_{{\mu _i}{\nu _j}}^\omega \left( {{\rm{1 - }}{\beta _q}} \right) \leqslant \overline Q _{{\mu _i}{\nu _j}}^\omega \leqslant Q_{{\mu _i}{\nu _j}}^\omega \left( {{\rm{1 + }}{\beta _q}} \right)\\ Q_{{\mu _i}{\nu _j}}^\omega E_{{\mu _i}{\nu _j}}^\omega \left( {{\rm{1 - }}{\beta _{eq}}} \right) \leqslant \overline Q _{{\mu _i}{\nu _j}}^\omega \overline E _{{\mu _i}{\nu _j}}^\omega \leqslant Q_{{\mu _i}{\nu _j}}^\omega E_{{\mu _i}{\nu _j}}^\omega \left( {{\rm{1 + }}{\beta _{eq}}} \right)\end{array} $(20)

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    $\begin{array}{l} {\beta _q} = \dfrac{{{n_a}}}{{\sqrt {N_{{\mu _i}{\nu _j}}^\omega Q_{{\mu _i}{\nu _j}}^\omega } }}\;\;\;\;\;\;\;\;{\beta _{eq}} = \dfrac{{{n_a}}}{{\sqrt {N_{{\mu _i}{\nu _j}}^\omega Q_{{\mu _i}{\nu _j}}^\omega E_{{\mu _i}{\nu _j}}^\omega } }}\end{array} $(21)

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    ${f_q} = {P_{{\mu _a}}}{P_{z|{\mu _a}}}{P_{{\mu _b}}}{P_{{\textit{z}}|{\mu _b}}}$(22)

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    Tianxiu Li, Lei Shi, Jiahao Li, Junhui Wang. Performance of Measurement Device Independent Quantum Key Distribution on flight repeater platform[J]. Infrared and Laser Engineering, 2021, 50(11): 20210124
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