Entanglement production under electron phonon interaction in a quantum dot

We consider the quantum dot entangler device introduced by Oliver et al. [1] coupled to a single phonon mode. While we take the phonon interaction to all orders, we perform a fourth order calculation in electron-dot coupling. Using the Von Neumann entropy we measure the degree of entanglement. We find that the phonon mechanism habilitates single electron processes which manifest themselves as decoherent processes.