In comparison to conventional discrete-variable (DV) quantum key distribution (QKD), continuous-variable (CV) QKD with homodyne/heterodyne measurements has distinct advantages of lower-cost implementation and affinity to wavelength division multiplexing. On the other hand, its continuous nature makes it harder to accommodate to practical signal processing, which is always discretized, leading to lack of complete security proofs so far. Here we propose a tight and robust method of estimating fidelity of an optical pulse to a coherent state via heterodyne measurements. We then construct a binary phase modulated CV-QKD protocol and prove its security in the finite-key-size regime against general coherent attacks, based on proof techniques of DV QKD. Such a complete security proof is indispensable for exploiting the benefits of CV QKD.

与常规离散变量（DV）量子密钥分配（QKD）相比，具有零差/外差测量的连续变量（CV）QKD具有成本低廉且对波分复用具有亲和力的明显优势。另一方面，它的连续性使其很难适应实际的信号处理，而信号处理始终是离散的，从而导致迄今为止缺乏完整的安全证明。在这里，我们提出了一种紧密而稳健的方法，可以通过外差测量将光脉冲保真度估计为相干态。然后，基于DV QKD的证明技术，我们构建了一个二进制相位调制CV-QKD协议，并证明了它在有限密钥大小体制下针对一般相干攻击的安全性。这样的完整安全性证明对于利用CV QKD的好处是必不可少的。