Fault-tolerant fusing of repeater graph states and its application

A repeater graph state (RGS) is a class of multipartite entangled states with favourable features for quantum communication, particularly as the enabler of all-photonic quantum repeaters. In this paper, based on an alternative formalism, we show that two RGSs can be fused via a Bell measurement in a fault-tolerant manner. The fusing of multiple RGSs can thus be carried out simultaneously and flexibly, which enables a 2-step rapid generation of an arbitrarily large RGS from relatively small building blocks using heralded but non-deterministic photonic Bell measurements. It then makes possible the distribution of a large multipartite entangled state from multiple sources to many parties via high-loss channels, and hence also a satellite-based entanglement distribution scheme. In such a scheme, stationary memories are only required for ground stations, the growth of memory noise with its scale can be effectively suppressed, and recipients of entangled pairs of qubits may remain anonymous.