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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年8月5日

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  • Yulin Chi,
  • Haiyu Ding,
  • Fei Wang,
  • Chengkang Pan,
  • Chunju Shao

摘要

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.