Optimising multipartite entanglement manipulation in quantum networks

Long-range, genuine multipartite entanglement (GME) between distant parties in a quantum network is a crucial resource for distributed quantum information processing. Through controlled manipulation of short-range GME states in the network via stochastic local operations aided by classical communication (SLOCC), long-range GME can be established between selected target nodes on demand. Optimizing such multipartite entanglement distribution protocols under constraints imposed by the network architecture, target-node set, and available resource budget is a key challenge in resource-efficient manipulation of GME. We present a general operational framework for manipulating GME in quantum networks by classifying the relevant networking operations into three broad primitives-inflation, deflation, and purification-reflecting their effect on the proliferation of GME through general bounds and illustrative examples. We show how these primitives can be combined to construct a broad class of multipartite quantum repeater protocols, enabling their systematic optimization, and demonstrate the framework with a simple example. Applying our approach to networks of Dür-Cirac-Tarrach states reveals a rich landscape of achievable end-to-end GME and accessible entanglement classes. More generally, our framework provides a systematic approach to the construction and optimization of multipartite quantum repeater protocols for scalable and resource-efficient GME distribution in quantum networks.