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This study establishes a fundamental limit for quantum network performance by identifying entanglement-generation speed as a function of both interface capacity and architectural replenishment rates. By deriving sharp bounds for fermionic Gaussian dynamics and validating them with explicit Ising-chain trajectories, the research clarifies how system architecture dictates the sustainability of high-speed entangling flux. These findings provide critical theoretical guidance for optimizing control models in scalable quantum communication protocols.
Interface Capacity and Architectural Replenishment Determine Entanglement-Generation Speed in Quantum Networks
arXiv:2608.19020v1 Announce Type: new Abstract: 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 $\sum_k|\dot\theta_k|\leq\frac12\|K_{AB}\|_*$ 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.
Abstract: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 $\sum_k|\dot\theta_k|\leq\frac12\|K_{AB}\|_*$ 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.
Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)
arXiv:2608.19020 [quant-ph]
(or arXiv:2608.19020v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.19020 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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