Quantum communication, as a key technology to ensure future communication security, attracts wide attention and continues to develop rapidly. However, secure and efficient quantum communication requires quantum nonlocal correlations. Quantum steering, a unique form of quantum correlation distinct from entanglement and Bell nonlocality, enables directional information transmission. If Alice and Bob share a quantum state, Alice may steer Bob, but Bob may not steer Alice in return. This property facilitates the construction of quantum networks and the design of communication channels with specific functions. The four-wave mixing (FWM) process uses a nonlinear medium to generate spatially separated, correlated light beams through nonlinear interactions between input optical beams and atoms, providing a foundation for exploring quantum entanglement and nonclassical correlations in photons. Recent studies by Jing's team have generated multipartite entangled quantum states by cascading multiple FWM processes, producing tripartite, quadripartite, hexapartite, and twelve-partite entanglement. Additionally, combining the FWM process with a linear beam splitter generates quadripartite, octapartite, and twelve-partite entanglement. He's group achieves manipulation of tripartite quantum steering through different combinations of the FWM process, the linear beam splitter, and the nonlinear beam splitter (FWM process). Using cascaded FWM processes in symmetric and asymmetric structures, they study the monogamy relation of steering. The diversity and significance of FWM processes in quantum optics offer abundant possibilities for advancing quantum information science. Quantum secret sharing leverages the principles of quantum mechanics to distribute secret information among multiple independent individuals. This approach allows secrets to be retrieved only through cooperation, making it possible to detect eavesdroppers or dishonest participants. Quantum steering can allocate steering among players based on task requirements, providing a secure foundation for quantum secret sharing. Thus, quantum steering plays a critical role in quantum secret sharing.

In this research, we study quadripartite quantum steering based on two independent FWM processes combined with one linear beam splitter (BS 1). First, with a fixed transmissivity $T_{\mathrm{1}}=\mathrm{0.5}$, we analyze how quadripartite quantum steering varies with the amplitude gain of the FWM. Next, we introduce an additional linear beam splitter, so that two linear beam splitters are combined with the two FWM processes. With the gain of the FWM process fixed, we then examine how quadripartite quantum steering changes with the transmissivity of the second linear beam splitter (BS 2).

In Scheme I, the symmetry between output modes results in the absence of (1+1)-mode steering, while (1+n)-mode and (n+1)-mode steering are abundant. However, when mode $\widehat{C}$ is transmitted through a noisy channel, the excess noise and losses imposed on it cause quantum state decoherence, leading to a reduction or even disappearance of quantum steering. This also prevents mode $\widehat{C}$ from acting alone as either the steering or the steered party. In Scheme II, adjusting the transmissivity of BS 2 allows for flexible manipulation of pairwise steering, enabling both one-way and bidirectional asymmetry. Additionally, the configuration of joint steering is more robust, supporting richer correlations.

Analyzing quadripartite quantum steering generated by two FWM processes with one or two linear beam splitters reveals extensive multipartite EPR steering in both schemes. In Scheme I, (1+1)-mode steering is absent, but the bipartite (1+n)- and (n+1)-mode steering configurations are abundant, enabling three-party and four-party quantum secret sharing. In Scheme II, by adjusting the transmissivity of BS 2, the pairwise steering is not only present but also can be flexibly manipulated, allowing for both one-way and bidirectional asymmetry. This configuration also enhances the abundance of joint steering, which strengthens the ability to establish correlations and manage information across multiple users. Additionally, the number of possible user combinations for secret sharing increases, providing greater flexibility and security in quantum secret sharing. These findings have important applications and implications for building more adaptable, reliable, and secure quantum communication networks.