Vibrational effects on the formation of quantum W states

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