We study the estimation of parameters in a quantum metrology scheme based on entangled many-body Unruh-DeWitt detectors. It is found that the precision for the estimation of Unruh effect can be enhanced via initial state preparations and parameter selections. It is shown that the precision in the estimation of the Unruh temperature in terms of the many-body-probe metrology is always better than the precision in two probe estimations. The proper acceleration for Bob's detector and the interaction between the accelerated detector and the external field have significant influences on the precision for the Unruh effect's estimation. In addition, the probe state prepared with more excited atoms in the initial state is found to perform better than less excited initial states. However, different from the estimation of the Unruh temperature, the estimation of the effective coupling parameter for the accelerated detector requires more total atoms but less excited atoms in the estimations.
We study the estimation of parameters in a quantum metrology scheme based on entangled many-body Unruh-DeWitt detectors. It is found that the precision for the estimation of Unruh effect can be enhanced via initial state preparations and parameter selections. It is shown that the precision in the estimation of the Unruh temperature in terms of the many-body-probe metrology is always better than the precision in two probe estimations. The proper acceleration for Bob's detector and the interaction between the accelerated detector and the external field have significant influences on the precision for the Unruh effect's estimation. In addition, the probe state prepared with more excited atoms in the initial state is found to perform better than less excited initial states. However, different from the estimation of the Unruh temperature, the estimation of the effective coupling parameter for the accelerated detector requires more total atoms but less excited atoms in the estimations.
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.
We develop a quantum metrological framework for optimizing the probing of the Unruh effect using uniformly accelerated two-level atomic probes. The acceleration-dependent factor generated during the atom--field interaction is encoded in the atomic state and can be estimated through repeated quantum measurements. For a fixed total probe time, which characterizes the available measurement resource, we optimize the interrogation time of individual probes, the initial atomic state, and the corresponding measurement basis to minimize the estimation uncertainty. We show that the achievable precision is governed by the Fisher information accumulated per unit probe time. Under a fixed total probe time, shorter evolution times of individual probes allow for more sequential measurements, leading to a significant improvement in the estimation precision. The optimal initial state and measurement basis depend on both the acceleration factor and the probe evolution time. In particular, the excited state provides superior sensitivity in the weak-acceleration regime, whereas the ground state becomes advantageous for sufficiently large acceleration and long interaction times. Furthermore, we determine the minimum total probe time required to resolve the acceleration-dependent signal associated with the Unruh effect and demonstrate that this requirement can be substantially reduced by employing atomic systems with larger transition dipole moments. Our results establish an optimized quantum metrological strategy for probing acceleration-induced quantum effects and provide a systematic approach toward the experimental investigation of the Unruh effect.
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.
The quantum Fisher information matrix (QFIM) is central to multiparameter quantum metrology, dictating the attainable sensitivity via the quantum Cramér-Rao bound. In this work, we investigate the ultimate precision limits for relativistic quantum thermometry in a bipartite system of uniformly accelerated Unruh-DeWitt detectors. Utilizing the symmetric logarithmic derivative (SLD) formalism within the QFIM framework, we analyze the individual and simultaneous estimation of the Unruh temperature T and the initial-state parameter Δ0. In the noiseless case, we demonstrate that these two parameters are quantum compatible, allowing the multiparameter quantum Cramér-Rao bound to be saturated without a loss of precision. We then examine the impact of environmental effects by comparing Markovian and non-Markovian dynamics. In the Markovian regime, dissipation leads to a monotonic degradation of estimation precision; conversely, non-Markovian memory effects induce temporal oscillations and transient precision enhancements due to information backflow. The robustness of the estimation protocols is further analyzed under correlated noisy channels, including amplitude damping, phase flip, and phase damping. We show that dissipative noise results in more significant precision loss than purely dephasing mechanisms, whereas classical correlations in the noise mitigate this degradation. Finally, we discuss the estimation of the detector energy-level spacing ω as a natural extension, highlighting its sensitivity to the environmental structure. Our results provide a unified framework for relativistic multiparameter quantum metrology within the context of open quantum systems.
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 A protocol for multipartite quantum clock synchronization is performed under the influence of Unruh thermal noise. The dynamics of multipartite quantum system consisting of Unruh–DeWitt detectors when one of the detectors is accelerated are obtained. To estimate the time difference between the clocks, the time probability is calculated and how the probability is influenced by the Unruh thermal noise and other factors is analyzed. It is shown that both relativistic motion and interaction between the atom and the external scalar field affect the choice of optimal number of excited atoms in the initial state, which leads to a higher clock adjustment accuracy. Time probabilities for different types of initial states approach the same value in the limit of infinite acceleration, while tend to different minimums with increasing number of atoms. In addition, the accuracy of clock synchronization using a pair of entangled clocks in two‐party system is always higher than in a multipartite system, while the optimal Z‐type multipartite initial state always performs better than the W‐type state.