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 $|0〉+\alpha |1〉$ with $\alpha =\left|\alpha \right|e^{i\varphi }$, we propose a scheme to prepare a class of three-qubit pure states. These states take the form of ${|\psi 〉}_{123}=c_0|000〉+c_1|100〉+c_2|010〉+c_3|001〉$. The coefficients $(c_0,$ $c_1,$ $c_2, \text{and} c_3)$ can be manipulated through interaction parameters $\left(\right|\alpha |,$ $\varphi , \text{and} T)$. In line with Xie and Eberly's work [Phys. Rev. Lett. 127, 040403 (2021)], we investigate the genuine tripartite entanglement for ${|\psi 〉}_{123}$ 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 ${|\psi 〉}_{123}$ 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 ${|\psi 〉}_{123}$ exhibits entanglement, steering remains unattainable in a substantial portion of the parameter space.