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.