Optimal two-mode coherent states in lossy quantum-enhanced metrology

Abstract

We investigate an optimal distance of two components in a two-mode coherent state for quantum phase estimation in lossy interferometry. The optimal difference is obtained by an economical point, representing the quantum Fisher information that we can extract per input energy. Using the formula of the quantum Fisher information over an input mean photon number, we show that the more loss there is in the interferometry, the less entanglement of the two-mode coherent state we need to prepare initially. It means that the optimal distance of the two-mode components decreases with more loss in the interferometry. We also show that the corresponding optimal measurement is not a simple detection scheme but it is necessary to have correlation measurement bases.