| Summary: | We consider two-dimensional networks composed of nodes initially linked by two-qubit mixed states. In these networks we develop a global error correction scheme that can generate distance-independent entanglement from arbitrary network geometries using rank-2 states. By using this method and combining it with the concept of percolation, we also show that the generation of long-distance entanglement is possible with rank-3 states. Entanglement percolation and global error correction have different advantages depending on the given situation. To reveal the trade-off between them we consider their application to networks containing pure states. In doing so we find a range of pure-state schemes, each of which has applications in particular circumstances: For instance, we can identify a protocol for creating perfect entanglement between two distant nodes. However, this protocol cannot generate a singlet between any two nodes. In contrast, we can also construct schemes for creating entanglement between any nodes, but the corresponding entanglement fidelity is lower. © 2010 The American Physical Society.
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