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

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) state based on the fine-grained steering inequality was proved Quantum Studies: Mathematics and Foundations9 175 (2022). Here we provide an experimental proposal to prepare the GGHZ state in a photon system. The measurement observables in each party can be realized by different polarization optical elements. By choosing the angles of the waveplates, our experimental proposal can observe the maximum quantum violation for any three-qubit GGHZ state. 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.