Universal nested quantum switch

The quantum switch is a basic network primitive that allows one to connect multiple nodes in a quantum network via a central node. We show that the same functionality can be achieved with a different geometry that does not rely on a powerful and large central unit, but instead utilizes evenly distributed resources. This approach is resilient against node failures. We provide a nested construction with logarithmically many qubits per node and a total of $O\left(n\log n\right)$ Bell pairs, in contrast to other distributed approaches based on pre-shared entanglement that scale as O(n ²). The construction achieves fully flexible pairwise connectivity, where the shared resource state can be locally transformed into n/2 arbitrarily distributed Bell states. We also present a graph state variant with just one qubit per node, which allows one to generate $O\left(n/{\log }^{2}n\right)$ Bell pairs.