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Monte Carlo-based security analysis for multi-mode continuous-variable quantum key distribution over underwater channel

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Abstract

With the booming development and application of ocean exploration and investigation, it has become more and more important to achieve underwater communications for the establishment of global networks. This paper deals with a Monte Carlo-based performance analysis on multi-mode continuous-variable quantum key distribution over underwater links, where Monte Carlo model can characterize the complex probability density of underwater components. Compared with previous studies carried out in single-mode setting, the multi-mode protocol admits higher secret key rate. Last but not least, using non-Gaussian operations, we further improve the performance of multi-mode protocol, since it increases and distills entanglement in Gaussian entangled states.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work is supported by the National Nature Science Foundation of China (Grant Nos. 61872390, 61972418), the Hunan Provincial Innovation Foundation for Postgraduate (Grant No. CX20210250), the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2021zzts0202), the Outstanding Youth Program of Education Department of Hunan (Grant No. 21B0228), and the Changsha Municipal Natural Science Foundation (Grant No. kq2202293).

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Authors and Affiliations

  1. School of Computer Science and Engineering, Central South University, Changsha, 410083, PR China

    Wei Zhao & Ronghua Shi

  2. School of Automation, Central South University, Changsha, 410083, PR China

    Xinchao Ruan, Ying Guo & Yiyu Mao

  3. College of Computer and Information Engineering, Central South University of Forestry and Technology, Changsha, 410004, China

    Yanyan Feng

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  1. Wei Zhao
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Correspondence to Yanyan Feng.

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Appendix

Appendix

The radiative transfer equation describing the propagation behavior of light can be defined as [20, 31]

$$\begin{aligned} \frac{dL(z,\theta ,\phi ,\lambda )}{dr}=-c(\lambda )L(z,\theta ,\phi ,\lambda )+L^E+L^I . \end{aligned}$$
(18)

Here, \(L(z,\theta ,\phi ,\lambda )\) denotes the light radiance at a point, z denotes the distance of the point from the transmitter, \(\theta \) denotes the polar angles, \(\phi \) denotes the azimuthal angles, \(\lambda \) is the wavelength of the light, and r is the radial distance to the source with the notation \(r=\frac{z}{\mathrm {cos}\theta }\). The three terms on the right side of Eq. (18) represent the annihilation photons from the beam, the elastic scattering and the inelastic scattering.

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Zhao, W., Shi, R., Ruan, X. et al. Monte Carlo-based security analysis for multi-mode continuous-variable quantum key distribution over underwater channel. Quantum Inf Process 21, 186 (2022). https://doi.org/10.1007/s11128-022-03533-6

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