ENTANGLEMENT PERCOLATION IN QUANTUM NETWORKS: HOW TO ESTABLISH LARGE DISTANCE QUANTUM CORRELATIONS?

Quantum communication networks consist of N distant nodes sharing a quantum state. By means of local operation in each node assisted by classical communication, the nodes try to transform the initial state into perfect quantum correlations, that later will be used to perform a quantum information task, such as quantum teleportation or quantum cryptography. Given a network, defined by a geometry of nodes and connections, it is crucial to understand whether it is possible to establish long-distance quantum correlations, in the sense that the correlations between two end points of the network do not decrease exponentially with the number of intermediate connections. In this contribution, we present our recent findings on the distribution of entanglement through quantum networks. In the case of one-dimensional chains of connected quantum systems, the results are hardly surprising: a non-exponential decay is possible only when the entanglement in the connections between nodes is larger than a maximally entangled state of two qubits. The picture becomes much richer and interesting for networks of dimension larger than one: long-distance correlations can be established even when the connecting nodes are not maximally entangled. Actually, the problem of establishing maximally entangled states between nodes is related to classical percolation in statistical mechanics. We show, then, that statistical concepts, such as percolation and phase transitions, can be used to optimize the entanglement distribution through quantum networks. Remarkably, the quantum features allow going beyond the known results for classical percolation, giving rise to a new type of critical phenomenon that we call entanglement percolation.