Security of the perfect quantum key distribution protocol can be guaranteed by applying the fundamental laws of quantum mechanics, but the practical quantum key distribution system may be attacked by utilizing the imperfect state preparation and measurement devices. In this work, we analyze security of the practical quantum key distribution system with weak randomness basis selection, where the basis selection may be partly controlled by the eavesdropper due to the imperfect quantum devices. We propose the parameter $ϵ$ to quantify the deviation value between the practical basis selection probability and the perfect basis selection probability, and the secret key rate of the practical quantum key distribution system is obtained under different $ϵ$ values. By applying the practical experimental parameters, the analysis result demonstrates that the maximal transmission distance will be reduced from $142$ km to $139$ km if $ϵ\le 0.1$, but no secret key can be generated in the case of $ϵ\ge 0.34$.

中文翻译：

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具有弱随机性基础选择的实用量子密钥分发的安全性

通过应用量子力学的基本定律可以保证完美的量子密钥分配协议的安全性，但是利用不完善的状态准备和测量设备可能会攻击实际的量子密钥分配系统。在这项工作中，我们分析了具有弱随机性基础选择的实际量子密钥分发系统的安全性，该基础选择可能由于不完善的量子设备而被窃听者部分控制。我们提出参数$ϵ$ 量化实用基础选择概率与理想基础选择概率之间的偏差值，得到不同条件下实用量子密钥分配系统的秘密密钥率 $ϵ$价值观。通过应用实际的实验参数，分析结果表明最大传输距离将减小$142$ 公里到 $139$ 公里，如果 $ϵ\le 0.1$，但在以下情况下无法生成密钥： $ϵ\ge 0.34$。