Quantum correlations and metrological advantage among Unruh-DeWitt detectors in de Sitter spacetime

A long-standing debate on Gibbons-Hawking (GH) decoherence centers on its unclear thermal nature. In this work, we investigate the robustness of quantum Fisher information (QFI) and local quantum uncertainty (LQU) in the presence of GH decoherence, using free-falling Unruh-DeWitt (UDW) detectors in de Sitter spacetime (dS-ST). The UDW detectors interact with a massless scalar field in dS-ST and are modeled as open quantum systems, with the field acting as the environment for which we use a master equation to describe their evolution. Our analysis investigates the roles of energy spacing, GH temperature, initial state preparation, and various de Sitter-invariant vacuum sectors on the optimization of QFI and LQU. We find that the optimal values of QFI and LQU depend on the selected de Sitter-invariant vacuum sector and increase with larger energy spacing. Our findings reveal that QFI exhibits resilience to GH decoherence, maintaining a pronounced local peak across a wider range of parameters. This robustness can be further enhanced through strategic initial state preparation and increased energy spacing, resulting in a higher maximum QFI value even under significant environmental decoherence. Our results underscore the critical role of GH thermality in governing QFI and LQU, offering valuable insights for advances in relativistic quantum metrology (RQM).