The entanglement of damped noon-state and its performance in phase measurement

The state evolution of the initial optical \textit{noon} state is investigated. The residue entanglement of the state is calculated after it is damped by amplitude and phase damping. The relative entropy of entanglement of the damped state is exactly obtained. The performance of direct application of the damped \textit{noon} state is compared with that of firstly distilling the docoherence damped state then applying it in measurement.