We study the dynamics of quantum coherence under Unruh thermal noise and seek under which condition the coherence can be frozen in a relativistic setting. We find that the frozen condition is either (i) the initial state is prepared as a incoherence state, or (ii) the detectors have no interaction with the external field. That is to say, the decoherence of detectors' quantum state is irreversible under the influence of thermal noise induced by Unruh radiation. It is shown that quantum coherence approaches zero only in the limit of an infinite acceleration, while quantum entanglement could reduce to zero for a finite acceleration. It is also demonstrated that the robustness of quantum coherence is better than entanglement under the influence of the atom-field interaction for an extremely large acceleration. Therefore, quantum coherence is more robust than entanglement in an accelerating system and the coherence type quantum resources are more accessible for relativistic quantum information processing tasks.Comment: 6 pages, 2 figure

Clock synchronization between the ground and satellites is a fundamental issue in future quantum telecommunication, navigation, and global positioning systems. Here, we propose a scheme of near-Earth orbit satellitebased quantum clock synchronization with atmospheric dispersion cancellation by taking into account the spacetime background of the Earth. Two frequency entangled pulses are employed to synchronize two clocks, one at a ground station and the other at a satellite. The time discrepancy of the two clocks is introduced into the pulses by moving mirrors and is extracted by measuring the coincidence rate of the pulses in the interferometer. We find that the pulses are distorted due to effects of gravity when they propagate between the Earth and the satellite, resulting in remarkably affected coincidence rates. We also find that the precision of the clock synchronization is sensitive to the source parameters and the altitude of the satellite. The scheme provides a solution for satellite-based quantum clock synchronization with high precision, which can be realized, in principle, with current technology.

Quantum metrology studies the ultimate limit of precision in estimating a physical quantity if quantum strategies are exploited. Here we investigate the evolution of a two-level atom as a detector which interacts with a massless scalar field using the master equation approach for open quantum system. We employ local quantum estimation theory to estimate the Unruh temperature when probed by a uniformly accelerated detector in the Minkowski vacuum. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over all possible detector preparations and evolution times, and compare its behavior with that of the quantum Fisher information (QFI). We find that the optimal precision of estimation is achieved when the detector evolves for a long enough time. Furthermore, we find that in this case the FI for population measurement is independent of initial preparations of the detector and is exactly equal to the QFI, which means that population measurement is optimal. This result demonstrates that the achievement of the ultimate bound of precision imposed by quantum mechanics is possible. Finally, we note that the same configuration is also available to the maximum of the QFI itself.

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.I t is well known that a uniformly accelerated detector which interacts with external fields becomes excited in the Minkowski vacuum. This effect is named as Unruh effect 1,2 , which indicates the fact that quantum properties of fields is observer dependent 3-9 . However, despite its crucial role in modern theoretical physics, the experimental detection of the Unruh radiation remains an open research program on date. The main technical obstacle is that the Unruh temperature for the current experimental realizable acceleration lies far below the observable threshold of temperature. More specifically, the Unruh temperature is smaller than 1 Kelvin even for accelerations up to 10 21 m/s 2 2,10,11 . On the other hand, quantum metrology 12 aims to study the bounds of the estimation precision and the quantum strategies that can attain them. The estimation is based on measurements made on a probe system that undergoes an evolution depending on the estimated parameters. For a classical metrology scheme, the effect of statistical errors can be reduced by repeating the measurements and averaging the outcomes. Furthermore, by using some quantum resources and taking into account laws of quantum mechanics, the precision can be enhanced. More specifically, the mean variance of the errors for a given measurement on the parameter h is bounded by the Cramér-Rao inequality 13 Var h ð Þ § nF j h ð Þ ½ {1 , where n is the number of identical measurements repeated and F j h ð Þ is the Fisher information (FI) for a given measurement scheme. Moreover, by optimizing over all the possible set of quantum measurements, the ultimate limit on the variance is set by the quantum Cramér-Rao bound Var h ð Þ § nF Q h ð Þ ½ {1 , where F Q h ð Þ §F j h ð Þ is the quantum Fisher information (QFI). Recently, the adaptation of quantum metrology to improve probing technologies of relativistic effects has been preceded by several pioneering works in different contexts, see for example [14][15][16][17][18][19][20][21][22] . These studies are of great importance for the observation of ...

Modeling the qubit by a two-level semiclassical detector coupled to a massless scalar field, we investigate how the Unruh effect affects the nonlocality and entanglement of two-qubit and threequbit states when one of the entangled qubits is accelerated. Two distinct differences with the results of free field model in non-inertial frames are (i) for the two-qubit state, the CHSH inequality can not be violated for sufficiently large but finite acceleration, furthermore, the concurrence will experience "sudden death"; and (ii) for the three-qubit state, not only the entanglement vanishes in the infinite acceleration limit, but also the Svetlichny inequality can not be violated in the case of large acceleration.