Multipartite product-state analogue of genuine nonlocality without entanglement

Determine whether an analogous phenomenon of two globally distinguishable but locally indistinguishable multipartite product states can occur for any number of states.

Background

The paper constructs pairs of multipartite product measurements that are globally perfectly distinguishable but remain indistinguishable by finite-round LOCC across every bipartition, even when the parties on either side may act jointly.

The authors contrast this result with multipartite product-state discrimination and state that, to their knowledge, the analogous phenomenon has not been demonstrated for any number of product states. This leaves unresolved whether such a state-based counterpart exists.