Fig. 1

An EPR pair and a residual graph state (b) are distilled from a cluster state with 9 qubits (a) using the X-protocol (orange) on the path (1, 2, 5, 6, 9). Note that the combined neighborhood of nodes 1 and 9 is just the set {1, 9} after the qubits corresponding to nodes 2, 5, 6 are X-measured. The X-protocol in terms of local complementations is visualized in Fig. 3. The repeater protocol (blue) on the same path isolates the path (c) yielding the EPR pair between nodes 1 and 9 (d) after the measurement of the intermediate nodes 2, 5, 6