Estimation of decoherence in electromechanical circuits

Highlights: • Formulation of Hamiltonian Kerr in an Electromechanical circuit. • Dynamical in quantum open systems. • Bipartite entanglement of continuous variables. • Estimation of the Decoherence via Fisher information. • Phase sensitivity via the Cramer-Rao inequality. -- Abstract: This letter presents a schematic circuit with capacitive coupling between the CPW Cavity Center Trace (resonated with electromagnetic mode) and the mechanical Nanoresonator mediated by Transmon, resulting in the Cross-Kerr electromechanical effect. Then we show the dynamics of quantum states, showing the generation of superposition states and bipartite entanglement of continuous variables through nonlinear quantum electrodynamics in the circuit. Finally, we calculated and estimated the parameter for mechanical outcome through phase measurements of the CPW Cavity Center Trace electromagnetic mode.