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arXiv:1801.01666 · Annalen der Physik

Multipartite Quantum Clock Synchronization under The Influence of Unruh Thermal Noise

Li Zhang, Jiliang Jing, Heng Fan, Jieci Wang

Published Jun 24, 2019• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1002/andp.201900067

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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.
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 an incoherence state or (ii) the detectors have no interaction with the external field. That is to say, the decoherence of the 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.
It is well known that the quantum fluctuation of entanglement (QFE) between Unruh–De Witt detector (modeled by a two-level atom) is always investigated in a relativistic setting. However, both of the Unruh radiation and quantum fluctuation effects play an important role in precise measurements of quantum entanglement. In this paper, we have quantitatively analyzed how the relativistic motion affects the QFE for two entangled Unruh–De Witt detectors, one of which is accelerated and interacting with the neighbor external scalar field. Our results show that the QFE, which initially increases by the Unruh thermal noise, will suddenly decay when the acceleration reaches to a considerably large value. Therefore, the relativistic effect will lead to non-negligible QFE effect. We also find that the initial QFE (without acceleration effect) reaches its minimum value at the maximally entangled state and the separable state. More importantly, our analysis demonstrates that although the QFE has a huge decay when the acceleration is greater than ∼0.96, the ratio of ΔE/C is still very large, due to the simultaneous decay of concurrence to a very low value. Finally, enlightened by the well-known equivalence principle, we discuss the possibility of applying the above findings to the dynamics of QFE under the influence of gravitation field.
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.
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.
Abstract Quantum coherence of the tripartite W state and Greenberger–Horne–Zeilinger (GHZ) state under the Unruh effect are explored based on the model of a two‐level detector qubit coupled to a massless scalar field. The results reveal that Unruh thermal noise really destroys tripartite quantum resources. It is worth mentioning that the quantum coherence of the GHZ state reaches zero in the infinite acceleration limit, but that of the W‐state always remains nonzero. Coherence of the GHZ state displays a sudden death as the coupling parameter grows, while coherence freezing can be witnessed for the W state. It can be concluded that the W state is more robust than the GHZ state against Unruh radiation. Moreover, the related investigation can be expanded to N‐qubit quantum systems and the corresponding analytical solution is obtained. It indicates that the larger number W‐type entangled qubit can be as a better quantum resource for quantum information tasks under the Unruh effect.
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.