An experimental proposal certification for any three-qubit generalized Greenberger-Horne-Zeilinger states based on the fine-grained steering inequality

Abstract Multi-party quantum steering is an important concept in quantum information theory and quantum mechanics, typically related to quantum entanglement and quantum nonlocality. It enables precise manipulation of large quantum systems, which is essential for large-scale quantum computing, simulations, and quantum communication. Recently, a quantum steering certification for any three-qubit generalized Greenberger-Horne-Zeilinger (GGHZ) states based on the fine-grained steering inequality was proved [Quantum Studies: Mathematics and Foundations, 2022, 9(2): 175-198]. Here we provide an experimental proposal to prepare the GGHZ states in photon system. The measurement observalbes in each party can be realized by different polarization optical elements. By choosing the angles of the waveplates, our experiment proposal can observe the maximum quantum violation for any three-qubit GGHZ states. Our proposal can be easily extended to high-dimensional qubits and multi-photon GHZ states, which provides a method to study the complex multi-party quantum protocols.