Exploring the boundary of quantum network states from inside out

Quantum networks with bipartite resources and shared randomness present the simplest infrastructure for implementing a future quantum internet. Here, we shall investigate which kinds of entanglement can or cannot be generated from this kind of quantum network by examining their fidelity with different graph states. On the one hand, based on a standard form of graph states under local complementation and a fine-grained uncertainty relation between two projections, we establish upper bounds of fidelity that improve upon previous results by at least 25% as the dimension of local systems tends to infinity. On the other hand, in the triangle network, we propose efficient protocols to generate genuine multipartite entangled states from the network, providing significant nontrivial lower bounds of fidelity with high-dimensional GHZ states. Quantum networks with bipartite resources and shared randomness are important for the future quantum internet, yet the types of entanglement they can generate remain unclear. The authors establish improved upper bounds on fidelity for graph states and propose efficient protocols for generating genuine multipartite entangled states, enhancing quantum network capabilities.