Spanning-tree-packing protocol for conference key propagation in quantum networks

We consider a network of users connected by pairwise quantum key distribution (QKD) links. Using these pairwise secret keys and public classical communication, the users want to generate a common (conference) secret key at the maximal rate. We propose an algorithm based on spanning tree packing (a known problem in graph theory) and prove its optimality. This algorithm enables optimal conference key generation in modern quantum networks of arbitrary topology. Additionally, we discuss how it can guide the optimal placement of new bipartite links in the network design.