Stability of genuine multipartite network entanglement under catalytic local operations

Determine whether the notion of genuine multipartite network entanglement, as proposed for multipartite quantum states, is stable under catalytic local operations (CLO).

Background

The paper demonstrates that genuine multipartite entanglement (GME), although not creatable from biseparable states by ordinary local operations and classical communication, can be activated catalytically under CLO. In particular, every biseparable state that is not partition-separable can be transformed into a GME state with a catalyst, while partition-separable states cannot be activated in this way.

Because this catalytic instability challenges the operational meaning of the standard definition of GME, the paper points to genuine multipartite network entanglement as an alternative notion that is stable under taking multiple copies by construction. The unresolved issue is whether that alternative resource notion also remains invariant against catalytic local operations.