We theoretically investigate the formation of W states in a tripartite system composed of three charge qubits coupled to vibrational modes. The electromechanical coupling is responsible for second-order virtual processes that result in an effective electron-electron interaction between neighbor qubits, which leads to the formation of W states. Based on the Lang-Firsov transformation and perturbation theory, we analytically solve the quantum dynamics, providing a mathematical expression for the maximally entangled W state. Dephasing is also taken into account, paying particular attention to the robustness of bipartite entanglement against local dephasing processes.

中文翻译：

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振动对量子 W 态形成的影响

我们从理论上研究了W态在由三个与振动模式耦合的电荷量子位组成的三方系统中的形成。机电耦合负责导致相邻量子位之间有效电子-电子相互作用的二阶虚拟过程，从而导致形成W态。基于 Lang-Firsov 变换和微扰理论，我们解析解决了量子动力学，提供了最大纠缠W状态的数学表达式。移相也被考虑在内，特别注意二分纠缠对局部移相过程的鲁棒性。