量子网络中，界面容量与架构补充决定纠缠产生速度
Interface Capacity and Architectural Replenishment Determine Entanglement-Generation Speed in Quantum Networks
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中文总结 AI 辅助
该研究明确量子网络中纠缠产生速度由界面容量与架构补充能力共同决定，推导了费米子高斯动力学下的纠缠速度界，通过优化验证了架构对饱和深度的分类及VEEF方法的有效性。
中文摘要 AI 辅助
我们证明，固定网络界面上的纠缠产生速度受两种不同资源支配：界面自身的纠缠容量，以及周围架构为其补充新自由度的能力。对于费米子高斯动力学，我们推导了正则纠缠角集体速度的系数严格界：∑ₖ|θ̇ₖ| ≤ ½‖K_AB‖_*。明确的伊辛链重匹配轨迹达到该界，从而证明了在所述控制模型下的精确最小相互作用时间。超出高斯设定，对完整N=8的树-树族进行穷举优化表明，在固定界面容量、第一层纠缠、连通性和边预算下，饱和深度由有根架构精确分类。采用更高分辨率的仅x控制，变分纠缠增强场（VEEF）优化在双通道基准中达到数值解析的快-X最优值。在全部21个对称约化有根轨道中，预先指定的两时间VEEF增长诊断直接从优化动力学中恢复完整的补充划分。因此，界面容量决定可用的纠缠通量，而架构决定新自由度能否持续补充界面并维持该容量的重复使用。
英文摘要
We show that entanglement-generation speed across a fixed network interface is governed by two distinct resources: the entangling capacity of the interface itself and the ability of the surrounding architecture to replenish it with fresh degrees of freedom. For fermionic Gaussian dynamics, we derive the coefficient-sharp bound $\sum_k|\dotθ_k|\leq\frac12\|K_{AB}\|_*$ on the collective speed of the canonical entanglement angles. Explicit Ising-chain rematching trajectories saturate this bound, thereby certifying exact minimum interaction times under the stated control model. Beyond the Gaussian setting, exhaustive optimization of the complete $N=8$ tree--tree family shows that, at fixed interface capacity, first-layer entanglement, connectedness, and edge budget, the saturation depth is exactly classified by rooted architecture. With higher-resolution $x$-only control, variational entanglement-enhancing-field (VEEF) optimization reaches the numerically resolved fast-$X$ optimum in a two-channel benchmark. Across all 21 symmetry-reduced rooted orbits, a pre-specified two-time VEEF growth diagnostic recovers the complete replenishment partition directly from optimized dynamics. Interface capacity therefore sets how much entangling flux is available, whereas architecture determines whether fresh degrees of freedom can continually replenish the interface and sustain repeated use of that capacity.
