Qudit W and Greenberger-Horne-Zeilinger states on a two-photon chip.

High-dimensional quantum entangled states exhibit unique properties. While generalizations like qudit Bell, Greenberger-Horne-Zeilinger (GHZ), and Cluster states have been studied, the qudit W states remain underexplored. We discover that a superposition of qudit Dicke states can serve as high-dimensional generalizations of W states, demonstrating their enhanced robustness against qudit loss, and present linearly scalable quantum circuits for their generation. Using a programmable silicon-photonic entanglement generator, we first theoretically and experimentally demonstrate the generation of 3-ququart GHZ and W states using two photons and one ancillary ququart, with fidelities of 0.932 ± 0.009 and 0.901 ± 0.012, respectively. Genuine multipartite entanglement of the GHZ state and the improved resilience of the W state are confirmed. Our findings provide new insights and efficient approaches for qudit-based quantum science and technologies.