Figure 3. All-photonic quantum repeater protocol.

The protocol is defined as follows: (i) Alice (Bob) prepares m single photons that are maximally entangled with her (his) local qubits and sends them to the adjacent receiver node . At the same time, any other source node prepares the encoded complete-like cluster state , and the left (right) arms are sent to the left-hand (right-hand) adjacent receiver node . (ii) On receiving the single photons (this moment in the case of (m, n)=(3, 2) is snapshot as an example), every receiver node applies the Bell measurement of Fig. 2a to the m pairs of the 2nd-leaf qubits of the left and right arms. (iii) If one of the Bell measurements succeeds, the receiver node performs the loss-tolerant X-basis measurements on the 1st-leaf qubits on the successful arms, and makes the loss-tolerant Z-basis measurements on all the other 1st-leaf qubits. If all the m Bell measurements or one of the loss-tolerant measurements on the 1st-leaf qubits fails, the receiver node regards this trial as failure. (iv) Finally, the receiver nodes announce all the measurement outcomes to Alice and Bob, and the protocol succeeds when no receiver node judges this trial as failure.