From Physical to Logical: Graph-State-Based Connectivity in Quantum Networks

Entanglement is a key resource in quantum communication, but bipartite schemes are often insufficient for advanced protocols like quantum secret sharing or distributed computing. Graph states offer a flexible way to represent and manage multipartite entanglement in quantum networks, enabling logical connectivity through local operations and classical communication (LOCC). In this work, we extend existing approaches based on bi-star configurations to more complex multi-star topologies. We analyze the maximum connectivity that can be achieved in networks of $m$ switches, each connected to $n$ clients, including asymmetric cases where the number of clients varies per switch. We also propose methods to enable logical communication between distant nodes. Our results support the development of scalable quantum networks with rich connectivity beyond traditional bipartite structures.