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arXiv:2503.04230 · Physics Letters B

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

Yu-Kun Zhang, Tariq Aziz, Li-Juan Li, Xue‐Ke Song, Liu Ye, Dong Wang

Published Jan 13, 2026• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1016/j.physletb.2026.140167

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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.
Abstract We explore the quantum coherence between a pair of entangled Unruh–DeWitt detectors, interacting with a quantum field, using a nonperturbative approach in a (3+1)-dimensional Minkowski spacetime with instantaneous switching ( δ\delta δ δ -switching). It is intriguing to observe that for a maximally entangled state, increasing the coupling strength enhances the detectors’ initial quantum coherence while simultaneously causing a monotonic decrease in their initial entanglement. This reveals a remarkable phenomenon: through nonperturbative interactions, entangled Unruh–DeWitt detectors can exhibit a dual effect-amplifying quantum coherence while degrading quantum entanglement. This finding stands in stark contrast to previous studies based on perturbative methods or Gaussian switching functions, which generally concluded that interactions between detectors and the field lead to a simultaneous degradation of quantum coherence and entanglement due to environmental decoherence. Notably, while initially separable detectors successfully harvest quantum coherence from the vacuum, entanglement extraction remains fundamentally prohibited. These contrasting behaviors underscore the fundamental distinction between coherence and entanglement as quantum resources, and highlight their complementary roles in field-detector interactions.
An object moving with the acceleration will change the temperature of environment around it, because of the presence of the Unruh thermal effect. In this work, we investigate the impact of Unruh thermal noise on the quantum-memory-assisted entropic uncertainty and quantum correlation regarding a pair of Unruh-Dewitt detectors. Specifically, we examine how the acceleration, the coupling strength between the external field and the detector, and the initial state affect the uncertainty and the system's quantum discord. It turns out that the Unruh effect will result in the loss of the systemic quantumness and inflation of the uncertainty. Moreover, it is revealed that the uncertainty is reversely correlated with the system's quantum discord. Thereby, it is believed that our investigations provide new insights into understanding the behavior of objects in the relativistic background.
Quantum uncertainty is deeply linked to quantum correlations and relativistic motion. The entropic uncertainty relation with quantum memory offers a powerful way to study how shared entanglement affects measurement precision. However, under acceleration, the Unruh effect can degrade quantum correlations, raising questions about the reliability of QMA-EUR in such settings. Here, we investigate the QMA-EUR for two uniformly accelerating Unruh-DeWitt detectors coupled to a massless scalar field. Using the Kossakowski-Lindblad master equation, we calculate the entropic uncertainty, its lower bound, and the tightness of the relation under different Unruh temperatures. We find that acceleration does not always increase the lower bound on the uncertainty relation. Depending on the initial correlations between the detectors, it may either increase or decrease. This behavior results from the interplay between quantum discord and minimal missing information. Interestingly, a higher quantum discord does not necessarily lead to lower uncertainty.
Abstract A long-standing debate on Gibbons–Hawking (GH) decoherence centers on its obscure 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 serving as the environment, described by a master equation that outlines 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 broader 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).
Abstract This investigation focuses on studying the dynamics of entropy disorder and quantum correlations between two detectors interacting with a scalar field in a four-dimensional Minkowski space-time using the Unruh-deWitt model. The aim is to gain insights into the evolution of quantum resources in uniformly accelerated detectors that interact with a massless scalar field. To achieve this, useful metrics such as local quantum Fisher information (LQFI), quantum consonance, and linear entropy are employed to analyze the quantum correlations and entropy disorder. The results indicate that the quantum correlations are heavily reliant on the choice of the initial state of the detectors. Interestingly, the quantum correlations exhibit a surprising resurgence as the Unruh temperature increases for specific initial state parameters. However, for other values, the Unruh temperature takes over and leads to a monotonic decrease in the quantum correlations. In addition, the degree of disorder is observed to increase as the Unruh temperature increases. Furthermore, the investigation delves into how the energy spacing of the detector affects quantum correlations across various initial state parameters. Further elucidating the behavior of quantum resources in curved space-time, we demonstrate that some initial state parameters can cause sudden changes in correlation measures as a function of energy spacing. These results highlight the relevance of choosing adequate initial state parameters, as they have a significant impact on the variation of quantum resources in two Unruh-deWitt detectors.
Abstract The uncertainty principle limits the ability to simultaneously predict measurement outcomes for two non‐commuting observables of a quantum particle. However, the uncertainty can be violated by considering a particle as a quantum memory correlated with the primary particle. By modeling an Unruh–Dewitt detector coupled to a massless scalar field, it is explored how the Unruh effect affects the entropic uncertainty and the tighter lower bound for a pair of entangled detectors is probed when one of them is accelerated. It is found that Unruh thermal noise really gives rise to an increase of entropic uncertainty for the given conditions since the correlation between quantum memory and the measured system is decreased. It is shown that the bound of the entropic uncertainty relations, in the presence of memory, can be formulated by introducing the Holevo quantity and mutual information. It is also noticed that Adabi's lower bound is tighter than that of Berta, and just the optimal bound under the Unruh effect. Moreover, it is shown that Berta's lower bound is unrelated to the choice of complementary observables, while the optimal Adabi's lower bound is dependent on the measurement choice. It is worth mentioning that the investigations may offer a better understanding of the entropic uncertainty in a relativistic motion.