Scalable order-dependent deterministic entanglement swapping

Determine whether deterministic entanglement-swapping protocols exist that are simultaneously scalable to large quantum networks and dependent on the order of operations as measured by an entanglement measure.

Background

The paper finds explicit order dependence for deterministic entanglement concentration in some parallel continuous-variable networks, but its analyzed series examples have order-independent swapping outcomes. Operation order is important because different sequences can potentially produce different final entanglement values in general networks.

The conclusion identifies the existence of scalable deterministic swapping protocols with genuine entanglement-measure-based order dependence as an unresolved problem.