Quantum LAN: On-Demand Network Topology via Two-colorable Graph States

In Quantum Local Area Networks (QLANs) - the near-term building block of the Quantum Internet - the choice of the physical network topology is not so restrictive and binding as in classical LAN in terms of communication capabilities among the network nodes. And the rationale for this is the entanglement-enabled connectivity induced by multipartite entangled states. Indeed, it is possible to create on-demand links between the QLAN nodes by properly manipulating the shared multipartite entangled states. Thus, it is possible to build an overlay entangled network upon the physical one, characterized by a topology different from the physical one and referred to as artificial topology. In this paper we address the fundamental issue of engineering the artificial topology to bypass the limitations induced by the physical network topology. This possibility to overcome the constraints in the network design induced by the physical topology has no counterpart in classical networks. To this aim, we exploit the properties of a class of multipartite entangled states, referred to as graph states, which exhibit unique properties, making them very interesting and promising for engineering artificial topologies in QLANs.