On Matching in Multipartite Quantum Routers

Over the past few years, the concept of quantum routers and their usefulness in quantum communication networks (e.g., in the BB84 protocol [5]) has been popularized in quantum information theory. While quite some work has been done on the theoretical implementation of quantum routers using multiplexing, most of it is constrained to the bipartite case [2, 9]. We extend this setup to quantum routers used in multipartite conference key agreement protocols so as to distribute a secret key among N parties. We formalize the general quantum entanglement matching problem, and show it's NP-completeness. We then study special cases for which we found efficient algorithms. Finally, we consider the weighted case where the weights represent the qubit ages.