Where to Decide: Control-Plane Geometry in Coherence-Limited Quantum Networks

Abstract:Quantum networks are usually framed by two hardware limits: how fast entanglement can be heralded, and how long a memory can hold it. We establish a third, geometric limit: entanglement decoheres while control information travels, so the distance to whoever allocates resources enters the fidelity budget directly. We develop a functional-graph abstraction weighting each link by its predicted multiplicative contribution to end-to-end fidelity, separating global but delayed state from local and immediate state, and compare centralized against local allocation in a replicated discrete-event model. Centralized delivery latency grows with network diameter while local latency is nearly scale invariant, differing up to twenty-fold for short-range traffic; the coherence threshold at which a global view outweighs a fresh one does not shift across the tested sizes; and as heralding accelerates, the dominant cost moves into the control plane. Slot synchronization instead obeys the product of slot rate and one-way link delay, so it is bounded by repeater spacing rather than diameter. Controller placement, decision locality, repeater spacing and slot rate are physical design parameters, not implementation details.

arXiv:2609.23047 [quant-ph]

(or arXiv:2609.23047v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.23047 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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