We investigate the temperature encoding process of two-level probes in de Sitter spacetime within the framework of open quantum systems. From a quantum-metrological perspective, we quantify the temperature encoding rate, which characterizes the precision of estimating a temperature parameter with a fixed total probe time. The maximal encoding rate is obtained by optimizing the initial state, evolution time, and measurement basis of each probe. For a static probe separated by a finite distance from a freely falling observer, both the intrinsic Gibbons--Hawking temperature and the position-dependent Unruh temperature are encoded in the probe state. We find that the encoding rate of the effective temperature is equal to the sum of the encoding rates of the intrinsic temperature and the Unruh temperature associated with the probe's inherent acceleration. Interestingly, when the intrinsic temperature is sufficiently small, the encoding rate of the intrinsic temperature initially increases with the Unruh temperature, reaches a maximum, and then decreases to zero. Thus, a nonzero inherent acceleration does not necessarily suppress the encoding of the intrinsic temperature. Instead, there exists an optimal inherent acceleration at which its encoding rate is maximized. Furthermore, we investigate the encoding rate of the Unruh temperature and the minimum total probe time required to estimate it with sufficient precision as functions of the separation distance. We find that the required total probe time and the corresponding number of probes remain experimentally feasible even when the probes are located relatively far from the cosmological horizon, with a radial position as large as $0.1$ times the horizon radius.
We investigate the temperature encoding process of two-level probes in de Sitter spacetime within the framework of open quantum systems. From a quantum-metrological perspective, we quantify the temperature encoding rate, which characterizes the precision of estimating a temperature parameter with a fixed total probe time. The maximal encoding rate is obtained by optimizing the initial state, evolution time, and measurement basis of each probe. For a static probe separated by a finite distance from a freely falling observer, both the intrinsic Gibbons--Hawking temperature and the position-dependent Unruh temperature are encoded in the probe state. We find that the encoding rate of the effective temperature is equal to the sum of the encoding rates of the intrinsic temperature and the Unruh temperature associated with the probe's inherent acceleration. Interestingly, when the intrinsic temperature is sufficiently small, the encoding rate of the intrinsic temperature initially increases with the Unruh temperature, reaches a maximum, and then decreases to zero. Thus, a nonzero inherent acceleration does not necessarily suppress the encoding of the intrinsic temperature. Instead, there exists an optimal inherent acceleration at which its encoding rate is maximized. Furthermore, we investigate the encoding rate of the Unruh temperature and the minimum total probe time required to estimate it with sufficient precision as functions of the separation distance. We find that the required total probe time and the corresponding number of probes remain experimentally feasible even when the probes are located relatively far from the cosmological horizon, with a radial position as large as 0.1 times the horizon radius.
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.
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).
A bstract Relativistic quantum metrology studies the maximal achievable precision for estimating a physical quantity when both quantum and relativistic effects are taken into account. We study the relativistic quantum metrology of temperature in (3+1)-dimensional de Sitter and anti-de Sitter space. Using Unruh-DeWitt detectors coupled to a massless scalar field as probes and treating them as open quantum systems, we compute the Fisher information for estimating temperature. We investigate the effect of acceleration in dS, and the effect of boundary condition in AdS. We find that the phenomenology of the Fisher information in the two spacetimes can be unified, and analyze its dependence on temperature, detector energy gap, curvature, interaction time, and detector initial state. We then identify estimation strategies that maximize the Fisher information and therefore the precision of estimation.
Quantum thermometry based on single-qubit sensor configurations enables the precise estimation of the temperature of a cosmological Anti-de Sitter (AdS) spacetime. In this work, we characterize the achievable estimation accuracy using the Quantum Fisher Information (QFI) and the associated quantum signal-to-noise ratio. For the first time, we introduce an ancillary Unruh-DeWitt detector between the sensor and the thermal bath, enhancing thermometric sensitivity by channeling temperature-dependent information into the probe qubit's coherence. We examine how detector acceleration in AdS space and the choice of boundary conditions modify the probe's thermal sensitivity. Despite the differing geometries, a unified phenomenology emerges: we characterize the scaling of the QFI with respect to temperature, detector energy gap, spacetime curvature, and interaction time. Finally, we identify optimal state preparation and measurement strategies that maximize the QFI, thereby establishing the fundamental limits of precision for non-Markovian sensing in curved spacetime.
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.
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.