Transmission of multi-level time-bin encoded cluster states over 29 km of partially deployed optical fiber

The next generation of telecommunication networks will rely on the distribution of complex quantum resources to enable secure and transformative information processing, utilizing entanglement and superposition. Cluster states-multi-qubit entangled states that retain entanglement under local measurements-are the central resource for measurement-based quantum information processing and compelling for quantum networking applications including blind quantum computing and quantum key agreement. However, transmitting cluster states over optical fiber has remained elusive with previous approaches, as losses scale exponentially with the number of photons. Here, we report the first transmission of a four-qubit cluster state to two parties over a partially deployed single-mode fiber link. The qubits of this state are encoded in two photons with multi-level time-bins. We directly generate the cluster state by exploiting coherent control of a parametric generation process, rendering a resource-intensive controlled-phase gate obsolete. To enable processing of this state, we introduce beam splitting for time-bins via chirped pulse modulation-a novel, reconfigurable Fourier-domain pulse shaping technique. We certify genuine multi-qubit entanglement and demonstrate one-way computing primitives on the transmitted cluster state. Our approach achieves the transmission of cluster states over optical fiber, establishing complex quantum resources fully compatible with telecommunication infrastructure.