Entanglement percolation in quantum networks

Quantum networks are composed of nodes that can send and receive quantum states by exchanging photons. Their goal is to facilitate quantum communication between any nodes, something that can be used to send secret messages in a secure way, and to communicate more efficiently than in classical networks. These goals can be achieved, for instance, via teleportation. Here we show that the design of efficient quantum-communication protocols in quantum networks involves intriguing quantum phenomena, depending both on the way the nodes are connected and on the entanglement between them. These phenomena can be used to design protocols that overcome the exponential decrease of signals with the number of nodes. We relate the problem of establishing maximally entangled states between nodes to classical percolation in statistical mechanics, and demonstrate that phase transitions can be used to optimize the operation of quantum networks.