We study the multipartite quantum steering generated by the nonlinear process of three-photon parametric down-conversion in an optical cavity. We find that the genuine quadripartite quantum steering can be obtained in this nonlinear process, and the injected signal can improve the stability of quadripartite quantum steering. By using the criterion of multipartite quantum steering, we show that the quadripartite quantum steering can be produced in the case of three-photon spontaneous parametric down-conversion when the quantum property of the pump is considered. We also discuss the quantum steering properties in the case of single-seed, double-seed, and triple-seed configurations, respectively, in a wide range of parameters. The result may be helpful to better understand the quantum correlation among the optical fields generated by three-photon parametric down-conversion and has potential applications in quantum information processing.

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• Nonlinear optics
• Nonlocality
• Quantum correlations in quantum information
• Quantum entanglement
• Quantum optics