We propose a scheme that generalizes the loss scaling properties of twin-field or phase-matching QKD related to a channel of transmission ${\eta }_{total}$ from $\sqrt{{\eta }_{total}}$ to $\sqrt[2n]{{\eta }_{total}}$ by employing $n-1$ memory stations with spin qubits and $n$ beam-splitter stations including optical detectors. Our scheme’s resource states are similar to the coherent-state-based light-matter entangled states of a previous hybrid quantum repeater, but unlike the latter our scheme avoids the necessity of employing $2n-1$ memory stations and writing the transmitted optical states into the matter memory qubits. The full scaling advantage of this memory-assisted phase-matching QKD (MA-PM QKD) is obtainable with threshold detectors in a scenario with only channel loss. We mainly focus on the obtainable secret-key rates per channel use for up to $n=4$ including memory dephasing and for $n=2$ (i.e. $\sqrt[4]{{\eta }_{total}}$-MA-PM QKD assisted by a single memory station) for error models including dark counts, memory dephasing and depolarization, and phase mismatch. By combining the twin-field concept of interfering phase-sensitive optical states with that of storing quantum states up to a cutoff memory time, distances well beyond 700 km with rates well above ${\eta }_{total}$ can be reached for realistic, high-quality quantum memories (up to 1s coherence time) and modest detector efficiencies. Similarly, the standard single-node quantum repeater, scaling as $\sqrt{{\eta }_{total}}$, can be beaten when approaching perfect detectors and exceeding spin coherence times of 5s; beating ideal twin-field QKD requires 1s. As for further experimental simplifications, our treatment includes the notion of weak nonlinearities for the light-matter states, a discussion on the possibility of replacing the threshold by homodyne detectors, and a comparison between sequential and parallel entanglement distributions.

中文翻译：

---

记忆辅助远程相位匹配量子密钥分配

我们提出了一种方案，该方案概括了与传输信道有关的双场或相位匹配QKD的损耗定标特性 ${\eta }_{ŤØŤ\mathrm{一种}升}$ 从 $\sqrt{{\eta }_{ŤØŤ\mathrm{一种}升}}$ 至 $\sqrt[2ñ]{{\eta }_{ŤØŤ\mathrm{一种}升}}$ 通过雇用 $ñ-\mathrm{1个}$ 自旋量子位和 $ñ$分束器站，包括光学探测器。我们的方案的资源状态类似于先前的混合量子转发器的基于相干态的光物质纠缠态，但与后者不同，我们的方案避免了采用$2ñ-\mathrm{1个}$存储站，并将传输的光学状态写入物质存储量子位。在只有通道丢失的情况下，使用阈值检测器可以获得此内存辅助相位匹配QKD（MA-PM QKD）的全部缩放优势。我们主要关注每个渠道使用可获得的密钥率，最高$ñ=4$ 包括内存分相和 $ñ=2$ （即 $\sqrt[4]{{\eta }_{ŤØŤ\mathrm{一种}升}}$-MA-PM QKD（由单个存储站协助）用于错误模型，包括暗计数，存储器去相和去极化以及相位失配。通过将干扰相敏光学状态的双场概念与存储量子状态直至截止存储时间的概念结合在一起，距离远超过700 km，速率远高于${\eta }_{ŤØŤ\mathrm{一种}升}$可以获得逼真的高质量量子存储器（相干时间可达1s）和适中的检测器效率。同样，标准的单节点量子中继器，缩放为$\sqrt{{\eta }_{ŤØŤ\mathrm{一种}升}}$接近完美的检测器并超过5s的自旋相干时间时，可能会被打败；击败理想的双场QKD需要1s。至于进一步的实验简化，我们的处理包括对光物质状态的弱非线性的概念，讨论用零差探测器代替阈值的可能性以及对连续和平行纠缠分布进行比较的讨论。