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In experimental setups of continuous-variable quantum key distribution (CVQKD) independently modulating the amplitude and phase of coherent states, the ideal Gaussian modulation will be degraded into discretized polar modulation (DPM) due to the finite resolution of the driving voltages of electro-optical modulators. To compensate for the performance degradation induced by the joint effect of amplitude and phase discretization, linear optics cloning machine (LOCM) can be introduced on the receiver side to reduce the influence of channel excess noise. Implemented by linear optical elements, homodyne detection and controlled displacement, LOCM introduces extra noise that can be transformed into an advantageous one to combat channel excess noise by dynamically adjusting the relevant parameters into a suitable range. In this paper, the prepare-and-measure version of LOCM DPM-CVQKD is presented, where the incoming signal state enters a tunable LOCM before being measured by the nonideal heterodyne detector. The equivalent entanglement-based model is also established to perform security analysis, where the LOCM is reformulated into combination of the incoming signal state and a thermal state on a beam splitter. The composable secret key rate is derived to investigate the security of LOCM DPM-CVQKD. Simulation results demonstrate that the secret key rate is closely related to the tuning gain and the transmittance of LOCM. Once these two parameters are set to appropriate values, LOCM can improve the secret key rate of DPM-CVQKD, and its resistance to excess noise. Meanwhile, taking finite-size effect into consideration, the LOCM can also effectively reduce the requirement for the block size of the exchanged signals, which is beneficial to the feasibility and practicability of CVQKD. Owing to the fact that the performance of LOCM DPM-CVQKD is largely reliant on the calibration selection of relevant parameters, further research may concentrate on the optimization of LOCM in experimental implementations, where machine learning related methods may be utilized.
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Keywords:
- quantum key distribution /
- continuous variable /
- discretized polar modulation /
- linear optics cloning machine
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图 1 LOCM DPM-CVQKD的制备测量方案
Figure 1. The PM scheme of LOCM DPM –CVQKD protocol.
图 2 LOCM DPM-CVQKD的纠缠等价方案
Figure 2. The EB scheme of LOCM DPM-CVQKD protocol.
图 3 LOCM对DPM-CVQKD可组合安全密钥率的改进
Figure 3. Enhancement of LOCM on the composable secret key rate of DPM-CVQKD.
图 4 LOCM对DPM-CVQKD可容忍过量噪声的改进.
Figure 4. Enhancement of LOCM on the tolerable excess noise of DPM-CVQKD.
图 5 调制方差对最大传输距离的影响, 幅值分辨率和相位分辨率分别设置为${\delta _{\text{a}}} = 0.25$, ${\delta _{\text{p}}} = 0.02$
Figure 5. The effect of modulation variance on maximum transmission distance, the amplitude resolution and phase resolution are ${\delta _{\text{a}}} = 0.25$, ${\delta _{\text{p}}} = 0.02$, respectively.
图 6 LOCM参数对可组合安全密钥率的影响, 幅值分辨率和相位分辨率分别设置为${\delta _{\text{a}}} = 0.25$, ${\delta _{\text{p}}} = 0.02$
Figure 6. Effect of LOCM-related parameters on the composable secret key rate, the amplitude resolution and phase resolution are ${\delta _{\text{a}}} = 0.25$, ${\delta _{\text{p}}} = 0.02$, respectively.
图 7 LOCM参数对最大传输距离的影响, 幅值分辨率和相位分辨率分别设置为${\delta _{\text{a}}} = 0.25$, ${\delta _{\text{p}}} = 0.02$ (a)调谐增益$\lambda $与传输损耗的关系; (b)等效透射率$\tau $与传输损耗的关系
Figure 7. Effect of LOCM parameters on maximum transmission distance, the amplitude resolution and phase resolution are set to ${\delta _{\text{a}}} = 0.25$, ${\delta _{\text{p}}} = 0.02$, respectively: (a) The tuning gain $\lambda $ versus losses; (b) the equivalent transmittance $\tau $ versus losses.
图 8 不同传输距离下码长对可组合安全密钥率的影响, 幅值分辨率和相位分辨率分别设置为${\delta _{\text{a}}} = 0.25$, ${\delta _{\text{p}}} = 0.02$
Figure 8. Effect of block length on the composable secret key rate under different transmission distances, the amplitude resolution and phase resolution are set to ${\delta _{\text{a}}} = 0.25$, ${\delta _{\text{p}}} = 0.02$, respectively.
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