Vibrational Effects on the Formation of Quantum $W$ States

TL;DR

This paper theoretically explores how vibrational modes influence the formation of $W$ states in a tripartite charge qubit system, highlighting the role of electromechanical coupling and analyzing robustness against dephasing.

Contribution

It introduces an analytical framework for understanding $W$ state formation via vibrationally induced interactions using Lang-Firsov transformation and perturbation theory.

Findings

Effective electron-electron interactions enable $W$ state formation.

Analytical solutions for quantum dynamics are derived.

Robustness of bipartite entanglement against dephasing is analyzed.

Abstract

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 responsable for second order virtual processes that result in an effective electron-electron interaction between neighbor qubits, which yields 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 accout, paying particular attention on the robustness of bipartite entanglement against local dephasing processes.