Topology-dependent cost of multipartite entanglement preparation

Characterize the network-dependent entanglement cost of preparing and distributing the weak GHZ-type resource states used for multipartite nonlocal rotations, including its dependence on network architecture and the routing structure connecting the participating parties.

Background

The paper extends its bipartite repeat-until-success protocol to multipartite Pauli rotations by replacing weak Bell pairs with weak GHZ-type states shared among the participating nodes. Although the protocol structure carries over, the resource cost depends on how these multipartite states are prepared and distributed across a particular network.

The unresolved issue is to obtain a full characterization of this topology-dependent cost, potentially establishing an operational resource theory for multipartite distributed quantum simulation.

References

The associated resource cost, however, becomes network dependent, as preparing and distributing multipartite entangled states $\ket{\mathrm{GHZ}_\theta}$ depends on both the network architecture and the chosen measure of multipartite entanglement. A full characterization of this cost lies beyond the bipartite analysis developed here and is left for future work.

— Distributed Trotterization with optimal time-scaling entanglement cost  (2608.25896 - Feng et al., 26 Aug 2026) in Section “Multipartite Generalization” and Discussion