Effect of the gravitational redshift on the precision of phase estimation

Gravitational effects are inevitable as photons propagate in curved spacetime, and especially gravitational redshift can cause the distortion of photon wave packets, so it is very meaningful and necessary to study the controllable parameter estimation under the gravitational-redshift effect. Here, in correlated noisy channels under the effect of gravitational redshift, we analyze the precision of phase estimation of two-qubit system states which is introduced by a symplectic matrix for two-mode entangled states (two types of Werner-like states). We find that the gravitational redshift could decrease the precision of phase estimation of these two-qubit system states. Interestingly, by adjusting the correlation parameter of the channels and the initial entanglement, the precision of phase estimation in noisy channels under the influence of gravitational redshift could be enhanced. The larger the initial entanglement and the stronger the correlation of the channels, the higher the precision of phase estimation obtained. Particularly, for two types of Werner-like initial states, the phase estimation of the system is more robust for the Werner-like initial state $\mathrm{cos}(\frac{\ensuremath{\alpha}}{2})|01⟩+{e}^{i\ensuremath{\phi}}\mathrm{sin}(\frac{\ensuremath{\alpha}}{2})|10⟩$ as the strong enough gravitational-redshift effect.