High precision regions of phase sensitivity for the superposition of coherent fields

Abstract

We investigate the problem of parameter estimation for the superposition of coherent fields under perfect and lossy regimes. We show the optimal range for higher precision of phase estimation by exactly solving a model consisting of a Schrödinger-cat state (SCS) subject to zero-temperature under a decoherence effect due to a dissipative interaction with an environment. We find the phenomenon that the quantum Fisher information (QFI), namely, the precision of estimation, is slowly reduced with the environment effect and affected by the photon number effects. We find that revivals and retardation of the QFI loss may occur by adjusting the mean photon number, and increasing the photons strongly enhances the coherence and hence augments the resolution of the parameter estimation. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement between the coherent field and its environment is investigated during the dissipation. We show that partial entanglement trapping occurs during the dynamics depending on the mean photon number. These features make the SCS with a larger average number of photons a good candidate for implementation of schemes of quantum optics and information with high precision.