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 $\mid 0⟩+\alpha \mid 1⟩$ with $\alpha =\mid \alpha \mid e^{i\phi }$, we propose a scheme to prepare a class of three-qubit pure states. These states take the form of ${\mid \psi ⟩}_{123}=c_0\mid 000⟩+c_1\mid 100⟩+c_2\mid 010⟩+c_3\mid 001⟩$. The coefficients ($c_0$, $c_1$, $c_2$, and $c_3$) can be manipulated through interaction parameters ($\mid \alpha \mid$, $\phi$, and $T$). In line with Xie and Eberly’s work[Phys. Rev. Lett. 127, 040403 (2021)], we investigate the genuine tripartite entanglement for ${\mid \psi ⟩}_{123}$ by using the measure of concurrence fill. Drawing on Hao $\mathit{\text{et}}\mathit{\text{al.}}$'s research [Phys. Rev. Lett. 128, 120402 (2021)], we examine tripartite steering for ${\mid \psi ⟩}_{123}$ 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 ${\mid \psi ⟩}_{123}$ exhibits entanglement, steering remains unattainable in a substantial portion of the parameter space.