Black-box estimation of expanding parameter for de Sitter universe

We study the black-box parameter estimation of expanding parameters and the dynamics of Gaussian interferometric power for the de Sitter space. We find that the state between separated open charts can be employed as a probe state for the black-box quantum metrology. This is nontrivial because the open charts are causally disconnected and classical information can not be exchanged between them according to the general relativity. It is shown that the mass of the scalar field remarkably affects the accuracy of the black-box parameter estimation in the de Sitter space, which is quite different from the flat space case where the mass parameter does not influence the precision of estimation. Quantum discord is found to be a key resource for the estimation of the expanding parameter when there is no entanglement between the initially uncorrelated open charts. It is demonstrated that the role of the probe state between different open charts is quite distinct because the curvature effect of the de sitter space damages quantum resources for the initially correlated probe states, while it generates quantum resources for the initially uncorrelated probe states.