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In practical continuous-variable quantum key distribution (CVQKD) systems, due to environmental disturbance or some intrinsic imperfections of devices, inevitably the local oscillator (LO) employed in a coherent detection always fluctuates arbitrarily over time, which compromises the security and performance of practical CVQKD systems. In this paper, we investigate the performance of practical CVQKD systems with LO fluctuating randomly. By revising the measurement result of balanced homodyne detection and embedding fluctuation parameters into security analysis, we find that in addition to the average LO intensity, the fluctuation variance also severely affects the secret key rate. No secret key can be obtained if fluctuation variance is relatively large. This indicates that in a practical CVQKD, LO intensity should be well monitored and stabilized. Our research can be directly applied to improve the robustness of a practical CVQKD system as well as be used to optimize CVQKD protocols.
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