Quantum communication networks with bipartite entanglement sources

Quantum networks attract much interest now. One of obvious purposes of quantum networks is secure communications. The usual quantum key distribution (QKD) deals with bipartite communication, but scaling of QKD to network solutions is developed now. In the first part of the talk, we will consider networks of users connected by bipartite QKD links. Such networks already exist. A problem arises: Having a network of bipartite QKD links, how to generate a conference key at maximal rate? An optimal solution is given by a spanning-tree-packing protocol for conference key propagation.
The second part of the talk will be devoted to foreseeable future quantum networks with bipartite entanglement sources. Such networks provide more possibilities and problems to be considered. The problem of conference key distribution is still relevant for these networks (but with more possibilities). A fully quantum counterpart of this problem is the Greenberger-Horne-Zeilinger (GHZ) multipartite entangled state distillation. GHZ states find many cryptographic, metrologic and computational applications. Spanning tree packing protocol also can be used for GHZ distillation and is also optimal whenever the distributed bipartite entangled states are pure. For general (mixed) bipartite quantum states, we present fundamental bounds on the conference key distribution and GHZ distillation rates for such networks.