Deterministic Generation of Loss-Tolerant Photonic Cluster States with a Single Quantum Emitter

A photonic cluster state with a tree-type entanglement structure constitutes an efficient resource for quantum error correction of photon loss. But the generation of a tree cluster state with an arbitrary size is notoriously difficult. Here, we propose a protocol to deterministically generate photonic tree states of arbitrary size by using only a single quantum emitter. Photonic entanglement is established through both emission and rescattering from the same emitter, enabling fast and resource-efficient entanglement generation. The same protocol can also be extended to generate more general tree-type entangled states.