High efficiency continuous-variable quantum key distribution based on QC-LDPC codes

Ying Guo; Kangshuai Wang; Duan Huang; Xueqin Jiang

doi:10.3788/COL201917.112701

Journals >Chinese Optics Letters >Volume 17 >Issue 11 >Page 112701 > Article

Chinese Optics Letters
Vol. 17, Issue 11, 112701 (2019)

High efficiency continuous-variable quantum key distribution based on QC-LDPC codes

Ying Guo¹, Kangshuai Wang¹, Duan Huang^1,*, and Xueqin Jiang²

Author Affiliations

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

²School of Information Science and Technology, Donghua University, Shanghai 201620, China

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DOI: 10.3788/COL201917.112701 Cite this Article Set citation alerts

Ying Guo, Kangshuai Wang, Duan Huang, Xueqin Jiang, "High efficiency continuous-variable quantum key distribution based on QC-LDPC codes," Chin. Opt. Lett. 17, 112701 (2019) Copy Citation Text

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Abstract

Seeking good error correcting codes to improve the efficiency of continuous-variable quantum key distribution (CVQKD) reconciliation is a concerning issue. Due to the introduction of multidimensional reconciliation, the error correcting techniques in the classical binary-input additive white Gaussian noise channel are applicable to CVQKD. In this Letter, we apply the quasi-cyclic low-density parity-check (QC-LDPC) codes, which are specified in 5G protocol, to the reconciliation process. Simulation results show that the reconciliation efficiency can reach 92.6% when the code rate is 22/68 and the signal-to-noise ratio is 0.623. Such a new error correcting code points out a new direction for the development of CVQKD.

C P M = I_{1} = {[\begin{matrix} 0 & 1 & 0 & 0 & \dots & 0 \\ 0 & 0 & 1 & 0 & \dots & 0 \\ 0 & 0 & 0 & 1 & \dots & 0 \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ 0 & 0 & 0 & 0 & \dots & 1 \\ 1 & 0 & 0 & 0 & \dots & 0 \end{matrix}]}_{Z \times Z},

(1)

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H_{b} = {[\begin{matrix} a_{11} & a_{12} & \dots & a_{1 n} \\ a_{21} & a_{22} & \dots & a_{2 n} \\ ⋮ & ⋮ & ⋮ \\ a_{m 1} & a_{m 2} & \dots & a_{m n} \end{matrix}]}_{m \times n},

(2)

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P = {[\begin{matrix} P_{11} & P_{12} & \dots & P_{1 n} \\ P_{21} & P_{22} & \dots & P_{2 n} \\ ⋮ & ⋮ & ⋮ \\ P_{m 1} & P_{m 2} & \dots & P_{m n} \end{matrix}]}_{m \times n} .

(3)

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H = H_{b}^{(P_{i j})} = {[\begin{matrix} H_{b}^{(P_{11})} & H_{b}^{(P_{12})} & \dots & H_{b}^{(P_{1 n})} \\ H_{b}^{(P_{21})} & H_{b}^{(P_{22})} & \dots & H_{b}^{(P_{2 n})} \\ ⋮ & ⋮ & ⋮ \\ H_{b}^{(P_{m 1})} & H_{b}^{(P_{m 2})} & \dots & H_{b}^{(P_{m n})} \end{matrix}]}_{m Z \times n Z} .

(4)

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k_{b} \times Z_{c} \geq K^{*} .

(5)

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F_{2}^{8} \to S^{7} \subset R^{8},

(6)

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u = (b_{1}, b_{2}, \dots, b_{8}) \mapsto (\frac{{(- 1)}^{b_{1}}}{\sqrt{8}}, \frac{{(- 1)}^{b_{2}}}{\sqrt{8}}, \dots, \frac{{(- 1)}^{b_{8}}}{\sqrt{8}}),

(7)

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M (x, y) = \sum α_{i} (x, y) A_{i},

(8)

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I_{A B} = \frac{1}{2} \log_{2} (1 + SNR) = \frac{1}{2} \log_{2} (\frac{V + χ_{t o t}}{1 + χ_{t o t}}),

(9)

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R = I_{A B} - I_{E},

(10)

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χ_{B E} = S (ρ_{E}) - \int {d m}_{B} p (m_{B}) S (ρ_{E}^{m_{B}}),

(11)

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K = (1 - F E R) (β I_{A B} - χ_{B E}),

(12)

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Ying Guo, Kangshuai Wang, Duan Huang, Xueqin Jiang, "High efficiency continuous-variable quantum key distribution based on QC-LDPC codes," Chin. Opt. Lett. 17, 112701 (2019)

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