Abstract In this paper, we investigate the quantum coherence extraction between two accelerating Unruh–DeWitt detectors, coupling to a scalar field in (3 + 1)-dimensional Minkowski spacetime. We find that quantum coherence as a nonclassical correlation can be generated through the Markovian evolution of the detector system, just like quantum entanglement. However, with growing Unruh temperature, in contrast to monotonously degrading entanglement, we find that quantum coherence exhibits a striking revival phenomenon. For certain detectors’ initial state choices, the coherence measure will reduce to zero at first and then grow to an asymptotic value. We verify such coherence revival by inspecting its metrological advantage on the quantum Fisher information (QFI) enhancement. Since the maximal QFI bounds the accuracy of quantum parameter estimation, we conclude that the extracted coherence can be utilized as a physical resource in quantum metrology.
Abstract In this paper, we investigate the quantum coherence extraction between two accelerating Unruh–DeWitt detectors, coupling to a scalar field in (3 + 1)-dimensional Minkowski spacetime. We find that quantum coherence as a nonclassical correlation can be generated through the Markovian evolution of the detector system, just like quantum entanglement. However, with growing Unruh temperature, in contrast to monotonously degrading entanglement, we find that quantum coherence exhibits a striking revival phenomenon. For certain detectors’ initial state choices, the coherence measure will reduce to zero at first and then grow to an asymptotic value. We verify such coherence revival by inspecting its metrological advantage on the quantum Fisher information (QFI) enhancement. Since the maximal QFI bounds the accuracy of quantum parameter estimation, we conclude that the extracted coherence can be utilized as a physical resource in quantum metrology.
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 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.
The goal of quantum metrology is the exploitation of quantum resources, like entanglement or quantum coherence, in the fundamental task of parameter estimation. Here we consider the question of the estimation of the Unruh temperature in the scenario of relativistic quantum metrology. Specifically, we study two distinct cases. First, a single Unruh-DeWitt detector interacting with a scalar quantum field undergoes an uniform acceleration for a finite amount of proper time, and the role of coherence in the estimation process is analyzed. After this, we consider two initially entangled detectors, one of which is inertial while the other one undergoes acceleration. Our results show that the maximum of the Fisher information, thus characterizing the maximum possible precision according to Crammér-Rao bound, occurs only for small accelerations, while it decreases fast when acceleration increases. Moreover, the role of initial coherence ---in the single detector case---, or entanglement ---in the two detectors case---, is to decrease Fisher information. Therefore, under the considered protocol, internal coherence (or entanglement) is not a resource for estimating Unruh temperature. These unexpected results show that a detection of the Unruh effect can be even more challenge than previously thought. Finally, by considering the connection between Unruh effect and Hawking radiation, we discuss how our results can be understood in the context of the estimation of Hawking temperature.
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.
A long-standing debate on Unruh effect is about its obscure thermal nature. In this Letter, we use quantum Fisher information (QFI) as an effective probe to explore the thermal nature of Unruh effect from both local and global perspectives. By resolving the full dynamics of UDW detector, we find that the QFI is a time-evolving function of detector's energy gap, Unruh temperature TU and particularities of background field, e.g., mass and spacetime dimensionality. We show that the asymptotic QFI whence detector arrives its equilibrium is solely determined by TU, demonstrating the global side of Unruh thermality alluded by the KMS condition. We also show that the local side of Unruh effect, i.e., the different ways for the detector to approach the same thermal equilibrium, is encoded in the corresponding time-evolution of the QFI. In particular, we find that with massless scalar background the QFI has unique monotonicity in n=3 dimensional spacetime, and becomes non-monotonous for n≠3 models where a local peak value exists at early time and for finite acceleration, indicating an enhanced precision of estimation on Unruh temperature at a relative low acceleration can be achieved. Once the field acquiring mass, the related QFI becomes significantly robust against the Unruh decoherence in the sense that its local peak sustains for a very long time. While coupling to a more massive background, the persistence can even be strengthened and the QFI possesses a larger maximal value. Such robustness of QFI can surely facilitate any practical quantum estimation task.
We study the quantum metrology for a pair of entangled Unruh-Dewitt detectors when one of them is accelerated and coupled to a massless scalar field. Comparing with previous schemes, our model requires only local interaction and avoids the use of cavities in the probe state preparation process. We show that the probe state preparation and the interaction between the accelerated detector and the external field have significant effects on the value of quantum Fisher information, correspondingly pose variable ultimate limit of precision in the estimation of Unruh effect. We find that the precision of the estimation can be improved by a larger effective coupling strength and a longer interaction time. Alternatively, the energy gap of the detector has a range that can provide us a better precision. Thus we may adjust those parameters and attain a higher precision in the estimation. We also find that an extremely high acceleration is not required in the quantum metrology process.
Quantum Fisher information (QFI) associated with local metrology has been used to parameter estimation in open quantum systems. In this work, we calculated the QFI for a moving Unruh–DeWitt detector coupled with massless scalar fields in n-dimensional spacetime, and analyzed the behavior of QFI with various parameters, such as the dimension of spacetime, evolution time, and Unruh temperature. We discovered that the QFI of state parameter decreases monotonically from 1 to 0 over time. Additionally, we noted that the QFI for small evolution times is several orders of magnitude higher than the QFI for long evolution times. We also found that the value of QFI decreases at first and then stabilizes as the Unruh temperature increases. It was observed that the QFI depends on initial state parameter θ, and Fθ is the maximum for θ = 0 or θ = π, Fϕ is the maximum for θ = π/2. We also obtain that the maximum value of QFI for state parameters varies for different spacetime dimensions with the same evolution time.