发表机构
The Coding School dba Frontier Technology Institute; Department of Computer Science, University of Maryland, College Park, Maryland, USA（Frontier Technology Institute; 马里兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过精确模拟不同噪声下的 GHZ 会议密钥协商协议，发现 Pauli 错误组成决定其相对 BB84 的多体优势，并推导闭式速率证明噪声分散优于集中。
AI 中文摘要
基于 GHZ 态的会议密钥协商在一次网络使用中将共享密钥分发给 $N$ 方，而两两 BB84 协议需要 $N-1$ 次。该优势的存续性已针对参与方数量、损耗和拓扑结构进行了研究，但几乎总是在信道固定为去极化噪声的情况下进行。我们精确模拟了在去相位、振幅阻尼和去极化噪声下 $N = 3, 4, 5$ 的两种协议，发现交叉点由信道的 Pauli 错误组成决定，而非其身份：归一化到平均保真度后，振幅阻尼和去极化在每个组大小下的差异在约 1\% 以内，而去相位在 $N = 3$ 时可容忍约 $2.4$ 倍的额外噪声。我们推导了任意每方 Pauli 噪声下的闭式速率，并利用它证明将固定噪声预算集中在一个臂上严格劣于分散它，且将经销商角色分配给最干净的臂可将速率提高约 18\%。每个结果都由一个结构事实驱动：相位错误项是所有 $N$ 个臂的乘积，而比特错误项保持在一对局部。
英文摘要
GHZ-based conference key agreement distributes a shared key to $N$ parties in one network use, whereas pairwise BB84 needs $N-1$. The survival of that advantage has been studied against party number, loss, and topology, but almost always with the channel fixed at depolarizing. Simulating both protocols exactly for $N = 3, 4, 5$ under dephasing, amplitude damping, and depolarizing noise, we find the crossover is set by the channel's Pauli error composition, not its identity: normalized to average infidelity, amplitude damping and depolarizing agree to within about 1\% at each group size, while dephasing can tolerate roughly $2.4\times$ more at $N = 3$. We derive a closed-form rate for arbitrary per-party Pauli noise and use it to prove that concentrating a fixed noise budget on one arm is strictly worse than spreading it, and that giving the dealer role to the cleanest arm improves the rate by roughly 18\%. One structural fact drives every result: the phase-error term is a product over all $N$ arms, while the bit-error term stays local to a pair.
Comments12 pages, 6 figures, 3 tables
