Twin-field quantum key distribution (TF-QKD) and its variant protocols are highly attractive due to the advantage of overcoming the rate-loss limit for secret key rates of point-to-point QKD protocols. For variations of TF-QKD, the key point to ensure security is switching randomly between a code mode and a test mode. Among all TF-QKD protocols, their code modes are very different, e.g. modulating continuous phases, modulating only two opposite phases, and sending or not sending signal pulses. Here we show that, by discretizing the number of global phases in the code mode, we can give a unified view on the first two types of TF-QKD protocols, and demonstrate that increasing the number of discrete phases extends the achievable distance, and as a trade-off, lowers the secret key rate at short distances due to the phase post-selection.

由于克服了点对点QKD协议的秘密密钥速率的速率损失限制，双域量子密钥分发（TF-QKD）及其变体协议具有很高的吸引力。对于TF-QKD的变体，确保安全的关键是在代码模式和测试模式之间随机切换。在所有TF-QKD协议中，它们的代码模式非常不同，例如调制连续相位，仅调制两个相反的相位以及发送或不发送信号脉冲。在这里我们表明，通过在代码模式下离散全局相位的数量，我们可以对前两种类型的TF-QKD协议给出统一的看法，并证明增加离散相位的数量可以扩展可实现的距离，并且由于阶段后选择，权衡会降低短距离的秘密密钥速率。