Tripartite entanglement and tripartite steering in three-qubit pure states induced by vacuum–one-photon superpositions

Utilizing a tritter with variable parameter T and induced by vacuum--one-photon superpositions |0+α|1 with α=|α|e^iφ, we propose a scheme to prepare a class of three-qubit pure states. These states take the form of |ψ₁₂₃=c₀|000+c₁|100+c₂|010+c₃|001. The coefficients (c₀, c₁, c₂, and c₃) can be manipulated through interaction parameters (|α|, φ, and T). In line with Xie and Eberly's work [Phys. Rev. Lett. 127, 040403 (2021)], we investigate the genuine tripartite entanglement for |ψ₁₂₃ by using the measure of concurrence fill. Drawing on Hao et al.'s research [Phys. Rev. Lett. 128, 120402 (2022)], we examine tripartite steering for |ψ₁₂₃ under certain measurements based on the uncertainty relations criterion. We identify nine potential configurations exhibiting varying steerability across different parameter spaces. It is important to highlight that, while the state |ψ₁₂₃ exhibits entanglement, steering remains unattainable in a substantial portion of the parameter space.