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

TL;DR

This paper investigates how quantum Fisher information and local quantum uncertainty behave under Gibbons-Hawking decoherence in de Sitter spacetime, revealing their robustness and dependence on vacuum sectors, energy spacing, and initial states, with implications for relativistic quantum metrology.

Contribution

It demonstrates the resilience of quantum Fisher information against Gibbons-Hawking decoherence and explores how vacuum choices and system parameters optimize quantum metrological advantages.

Findings

QFI maintains a local peak despite decoherence

Optimal QFI depends on vacuum sector and energy spacing

Robustness of QFI can be enhanced through initial state and energy adjustments

Abstract

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).