Phase-encoded measurement-device-independent quantum key distribution with practical spontaneous-parametric-down-conversion sources

Chun Zhou, Wan-Su Bao, Wei Chen, Hong-Wei Li, Zhen-Qiang Yin, Yang Wang, and Zheng-Fu Han

Phys. Rev. A 88, 052333 – Published 26 November 2013

Abstract

Measurement-device-independent quantum key distribution (MDI-QKD) with weak coherent sources has been widely and meticulously analyzed. However, the analysis for MDI-QKD with spontaneous-parametric-down-conversion sources (SPDCS) is incomplete. In this paper, we propose two passive decoy protocols suitable for parameter estimation in MDI-QKD using SPDCS. By accounting for practical parameters of SPDCS with thermal distribution, we present an investigation on the performances of MDI-QKD under the active three-intensity decoy protocol, the passive two-intensity decoy protocol, and the modified passive three-intensity protocol, respectively. Phase randomization, inherently a prerequisite for decoy protocol, is taken into consideration for evaluating the overall quantum bit gain and quantum bit error rate. The numerical simulations show that the MDI-QKD using SPDCS with practical decoy protocols can be demonstrated to be comparable to the asymptotical case and has apparent superiority both in transmission distance and key generation rate compared to the one using weak coherent sources. Our results also indicate that the modified passive three-intensity decoy protocol can perform better than the active three-intensity decoy protocol in MDI-QKD using practical SPDCS.

Received 15 August 2013

DOI:https://doi.org/10.1103/PhysRevA.88.052333

Authors & Affiliations

Chun Zhou¹, Wan-Su Bao^1,*, Wei Chen^2,†, Hong-Wei Li^1,2, Zhen-Qiang Yin², Yang Wang¹, and Zheng-Fu Han^2,‡

¹Zhengzhou Information Science and Technology Institute, Zhengzhou 450004, China
²Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China

^*Author to whom all correspondence should be addressed: 2010thzz@sina.com
^†kooky@mail.ustc.edu.cn
^‡zfhan@ustc.edu.cn

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Vol. 88, Iss. 5 — November 2013

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Figure 1
The schematic diagram of the phase-encoded MDI-QKD protocol using triggered single-photon sources based on SPDC processes. Here, PDC represents the nondegenerate SPDC process, BS stands for the 50:50 beam splitter, and PM stands for the phase modulator. $r_{0}$ , $r_{1}$ , $s_{0}$ , and $s_{1}$ are the four single-photon detectors for performing Bell state measurement. $D_{A}$ and $D_{B}$ are the threshold detectors used for triggering signal pulses.Reuse & Permissions
Figure 2
Key rate comparison for phase-encoded MDI-QKD using WCS and SPDCS. The setup parameters are listed in Table . The dotted curve, obtained from Eqs. (28) and (29), represents the infinite decoy-state protocol using SPDCS with PND given by Eq. (5) The dash-dotted curve, obtained from Eq. (28) and Eqs. (2)–(7) in Ref. [41], represents the infinite decoy-state protocol using WCS. The solid curve, obtained from Eqs. (23, 24, 25, 26, 27), represents the modified passive three-intensity decoy protocol using SPDCS with PND given by Eqs. (9) and (10), where the intensities are chosen by $u_{A} = u_{B} = 147.577 \times 10^{- 3}, P_{μ_{A}}^{cor} = P_{μ_{B}}^{cor} = 0.12$ , and $u_{A}^{'} = u_{B}^{'} = 623.927 \times 10^{- 3}, P_{μ_{A}^{'}}^{cor} = P_{μ_{B}^{'}}^{cor} = 0.1$ . The dashed curve represents the active three-intensity decoy protocol using WCS, which is obtained from Eqs. (6), (7), and (28), where the intensities are chosen by $u_{A} = u_{B} = 0.2$ and $u_{A}^{'} = u_{B}^{'} = 0.5$ . The related formulas for overall gain and QBER can be found in Appendixes and .Reuse & Permissions
Figure 3
A comparison for the probability of emitting different numbers of photons between heralded SPDCS and WCS. Here, $P_{x}^{cor} = 0.405 844$ and $μ_{x} = 1.425 \times 10^{- 3}$ for the SPDCS while the intensity is $0.5$ for the WCS.Reuse & Permissions
Figure 4
Key rate comparison among the modified passive three-intensity decoy-state protocol, the active three-intensity decoy-state protocol, and the passive two-intensity decoy-state protocol for MDI-QKD using practical SPDCS. The setup parameters are listed in Table . The solid and dotted curve are plotted the same as in Fig. 2. The dash-dotted curve, which is obtained from Eqs. (6), (7), and (28), represents the active three-intensity decoy protocol using SPDCS with PND given by Eq. (5), where the intensities are chosen by $u_{A} = u_{B} = 0.577 \times 10^{- 3}, P_{μ_{A}}^{cor} = P_{μ_{B}}^{cor} = 0.432 837$ , and $u_{A}^{'} = u_{B}^{'} = 1.425 \times 10^{- 3}, P_{μ_{A}^{'}}^{cor} = P_{μ_{B}^{'}}^{cor} = 0.405 844$ . The dashed curve, plotted referring to Eqs. (13), (16), (17), (18), and (19), denotes the passive two-intensity decoy-state protocol using SPDCS with PND given by Eqs. (9) and (10), where the intensities are chosen by $u_{A} = u_{B} = 0.577 \times 10^{- 3}, P_{μ_{A}}^{cor} = P_{μ_{B}}^{cor} = 0.432 837$ , and $u_{A}^{'} = u_{B}^{'} = 790 \times 10^{- 3}, P_{μ_{A}^{'}}^{cor} = P_{μ_{B}^{'}}^{cor} = 0.1$ . The related formulas for overall gain and QBER can be found in Appendixes and .Reuse & Permissions
Figure 5
Key rate of MDI-QKD with statistical fluctuation under the modified passive three-intensity decoy-state protocol. The setup parameters are listed in Table . The solid curve is plotted the same as Fig. 2. The dashed curve is obtained from Eqs. (31), (32), (25), (26), and (27) for our modified passive three-intensity decoy-state protocol with different length of data $N$ . The related formulas for overall gain and QBER can be found in Appendixes and . In the simulations, we assume that five standard deviations ( $n_{α} = 5$ ) are used.Reuse & Permissions
Figure 6
Diagram of the basic setup for a photon-number distribution passing through a beamsplitter with transmittancy of $η$ .Reuse & Permissions

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