Approaching the ideal quantum key distribution with two-intensity decoy states

Chun-Hui Zhang, Sun-Long Luo, Guang-Can Guo, and Qin Wang

Phys. Rev. A 92, 022332 – Published 14 August 2015

Abstract

We present a scheme for the practical decoy-state quantum key distribution with heralded single-photon source. In this scheme, only two-intensity decoy states are employed. However, its performance can approach the asymptotic case of using infinite decoy states. We compare it with the standard three-intensity decoy-state method, and through numerical simulations, we demonstrate its significant improvement over the three-intensity method in both the final key rate and the secure transmission distance. Furthermore, when taking statistical fluctuations into account, a very high key generation rate can still be obtained even at a long transmission distance.

Received 31 March 2015

DOI:https://doi.org/10.1103/PhysRevA.92.022332

Authors & Affiliations

Chun-Hui Zhang^1,2, Sun-Long Luo³, Guang-Can Guo^1,4, and Qin Wang^1,2,4,*

¹Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
²Key Lab of Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Ministry of Education, Nanjing 210003, China
³Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, China
⁴Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China

^*qinw@njupt.edu.cn

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Vol. 92, Iss. 2 — August 2015

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Images

Figure 1
(a) Schematic experimental setup. MD: modulator; PR: polarization rotator; PBS: polarizing beam splitter; $D 1 - D 3$ : single-photon detector. (b) The left histogram represents the photon-number distributions of the nontriggered events $p_{μ}^{nt} (p_{μ^{'}}^{nt})$ , and the right corresponds to the photon-number distributions of the signal and decoy state used in our scheme. Here in the simulation, we set practical parameters $μ = 0.2, μ^{'} = 0.4, η_{A} = 0.75$ , and $d_{A} = 3 \times 10^{- 6} .$
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Figure 2
(a) The lower bound of $Y_{1}$ and (b) the upper bound of $e_{1}$ vs the transmission distance. We compare our scheme with the standard three-intensity decoy-state method with HSPS, and each curve in (b) has been normalized with the results of using infinite number of decoy states. Here, we set reasonable value for the (weaker) decoy source $(μ = 0.2)$ in the three-intensity decoy-state method, besides, by referring Eq. (9), we fix the relation between $μ$ and $μ^{'}$ with $μ = 2 μ^{'} (1 - η_{A}) .$
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Figure 3
The relative optimal intensities of the signal states. Here we set practical value for the (weaker) decoy source in the three-intensity decoy-state method, $μ = 0.2$ , and using the condition $μ = 2 μ^{'} (1 - η_{A})$ in our two-intensity decoy-state method by referring Eq. (9). The relative values here refer to the ratio between the optimal intensity by using two- or three- decoy-state methods and corresponding value in the asymptotic case of using infinite number of decoy states.
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Figure 4
Comparison of the key generation rates between using the standard three-intensity decoy-state method and our two-intensity scheme: (a) the absolute values of the final key rates with logarithm scale; (b) the relative values of final key generation rates, here the “relative” refers to the ratio between the key generation rate of using two- or three- decoy-state methods and corresponding value in the asymptotic case of using infinite number of decoy states. Here we set practical value $μ = 0.2$ for the (weaker) decoy source in the three-intensity decoy-state method, and fixing $μ = 2 μ^{'} (1 - η_{A})$ in our two-intensity decoy-state method by referring to Eq. (9).
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Figure 5
Comparison of the final key generation rates between (a) our two-intensity decoy-state scheme and (b) the standard three-intensity decoy-state method, both using HSPS and accounting for statistical fluctuations. The black solid curves refer to the case without considering statistical fluctuations, and the dash-dotted curves correspond to the cases of taking statistical fluctuations into account.
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