Fiber transmission of cluster states via multi-level time-bin encoding

The next generation of telecommunication networks will rely on the transmission of complex quantum states to enable secure and transformative information processing, utilizing entanglement and superposition. Cluster states - multipartite entangled states that retain entanglement under local measurements - are a vital resource for quantum networking applications such as blind photonic quantum computing, quantum state teleportation and all-photonic quantum repeaters. However, the transmission of cluster states over optical fiber has remained elusive with previous approaches. Here, we demonstrate the first transmission of a four-qubit cluster state over 25 km of single-mode fiber by using a two-photon multi-level time-bin encoding. We directly generate the state by exploiting coherent control of a parametric generation process, rendering a resource-intensive controlled-phase gate obsolete. To enable efficient and reconfigurable projective measurements on the multi-level time-bin encoded state, we introduce chirped-pulse modulation and implement the first time-bin beam splitter, allowing us to certify genuine multipartite entanglement and to demonstrate one-way computing operations. Our approach enables the transmission of complex quantum states over long-distance fibers, permitting the implementation of multipartite protocols and laying the foundation for large-scale quantum resource networks.