General non-Gaussian bound for repeated interface utilization

Develop a general non-Gaussian analytic bound on repeated interface utilization that captures the architecture-dependent replenishment structure beyond the finite family of quantum networks studied in the paper.

Background

The paper separates the entangling flux supplied by a fixed physical interface from the ability of the surrounding architecture to replenish that interface with fresh degrees of freedom. In the fermionic Gaussian setting, the authors establish an exact nuclear-norm speed bound, and in a finite family of N=8 tree–tree Ising networks they show that rooted internal topology determines whether the interface can be repeatedly saturated in two or three restricted layers.

The unresolved issue is to extend this architecture-sensitive replenishment picture beyond the finite enumerated family and beyond Gaussian dynamics by deriving a general analytic bound for repeated interface utilization in non-Gaussian quantum networks. Such a result would convert the observed relationship between interface capacity, rooted replenishment, and entanglement-generation speed into a broadly applicable theoretical framework.