Quantumness and entropic uncertainty for a pair of static Unruh-DeWitt detectors

The degradation of quantum resources due to environmental noise is a fundamental challenge in quantum information science. In relativistic settings, this noise is intrinsically linked to vacuum fluctuations. Here, we investigate this connection using a model of two Unruh-DeWitt detectors interacting with a scalar field in Minkowski spacetime. Specifically, we focus on Bell nonlocality, quantum coherence, the nonlocal advantage of quantum coherence, and measured uncertainty, examining their dependence on the detector-field energy ratio, the inter-detector distance, and the initial state parameter. Notably, our central finding is that vacuum fluctuations are the primary mechanism of decoherence. Moreover, while spatial separation induces decoherence, all quantum resources converge to a non-zero steady state at large distances, confirming the robustness of nonlocality. These insights provide a deeper understanding of quantumness in a relativistic framework and may contribute to the ongoing discussion on the black hole information paradox.