Intra-QLAN Connectivity via Graph States: Beyond the Physical Topology

In the near to mid future, Quantum Local Area Networks (QLANs) – the fundamental building block of the Quantum Internet – will unlike exhibit physical topologies characterized by densely physical connections among the nodes. On the contrary, it is pragmatic to consider QLANs based on simpler, scarcely-connected physical topologies, such as star topologies. This constraint, if not properly tackled, will significantly impact the QLAN performance in terms of communication delay and/or overhead. Thankfully, it is possible to create on-demand links between QLAN nodes, without physically deploying them, by properly manipulating a shared multipartite entangled state, namely, a graph state. Thus, it is possible to build an overlay topology, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">artificial topology</i> , upon the physical one, by only performing Local Operations and Classical Communication (LOCC). In this paper, we address the fundamental issue of engineering the artificial topology of a QLAN to bypass the limitations induced by the physical topology. The designed framework relays only on local operations, without exchanging signaling among the client nodes of the QLAN, which, in turn, would introduce further delays in a scenario very sensitive to the decoherence. Finally, by exploiting the artificial topology, it is proved that the troubleshooting is simplified, by overcoming the single point of failure, typical of classical LAN star topologies.