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Annalen der Physik

Entropic Uncertainty Relation for Dirac Particles in Garfinkle–Horowitz–Strominger Dilation Space–Time

Zuo-Yuan Zhang, Jin‐Ming Liu, Zhengfeng Hu, Yuzhu Wang

Published Sep 24, 2018• 20 citations
Publisher

Abstract

Abstract The quantum‐memory‐assisted entropic uncertainty relation for Dirac particles in the background of a Garfinkle–Horowitz–Strominger (GHS) dilation black hole is investigated, and the relationship between the entropy uncertainty and the quantum entanglement of a hybrid qubit–qutrit state in the GHS space–time analyzed. The results show that the physically accessible uncertainty increases while the inaccessible uncertainty decreases as the dilation parameter of the black hole enhances. Moreover, the evolution behavior of the uncertainty is inversely correlated with that of the entanglement between the quantum memory and the particle to be measured. Meanwhile, a method to steer the entropic uncertainty with the technique of weak measurement reversal is proposed. It is found that the uncertainty can be reduced effectively by adjusting the appropriate measurement strength. These findings may lead to a deeper understanding of entropy uncertainty dynamics, as well as its steering in a curved space–time.

DOI
10.1002/andp.201800208

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Abstract The quantum‐memory‐assisted entropic uncertainty relation for Dirac particles in the background of a Garfinkle–Horowitz–Strominger (GHS) dilation black hole is investigated, and the relationship between the entropy uncertainty and the quantum entanglement of a hybrid qubit–qutrit state in the GHS space–time analyzed. The results show that the physically accessible uncertainty increases while the inaccessible uncertainty decreases as the dilation parameter of the black hole enhances. Moreover, the evolution behavior of the uncertainty is inversely correlated with that of the entanglement between the quantum memory and the particle to be measured. Meanwhile, a method to steer the entropic uncertainty with the technique of weak measurement reversal is proposed. It is found that the uncertainty can be reduced effectively by adjusting the appropriate measurement strength. These findings may lead to a deeper understanding of entropy uncertainty dynamics, as well as its steering in a curved space–time.
The precision of measurements for two incompatible observables is limited due to the uncertainty principle; however, it can be improved with the assistance of quantum memory. In article number 1800208, by considering that a particle is initially entangled with the quantum memory in flat Minkowski space–time, and then the quantum memory freely falls toward a Garfinkle–Horowitz–Strominger (GHS) dilation black hole and locates near the event horizon, Zuo-Yuan Zhang and co-workers investigate the quantum-memory-assisted entropic uncertainty relation for Dirac particles in GHS dilation space–time.
Abstract We explore the tripartite entropic uncertainty and genuine tripartite quantumness of Dirac fields in the background of the Garfinkle–Horowitz–Strominger (GHS) dilation space-time. It is interesting to note that Hawking radiation leads to the decay of quantum nonlocality in the physically accessible region while preserving its total coherence. More importantly, it demonstrates an intrinsic trade-off relationship between the coherences of physically accessible and inaccessible regions. Moreover, we examine the effect of Hawking radiation on entropy-based measured uncertainty and find that stronger Hawking radiation causes the uncertainty in physically accessible regions to increase while decreasing the uncertainty in physically inaccessible regions. Therefore, our investigations may be beneficial to a better understanding of the system’s quantumness in a curved space-time. Combining relativity theory with quantum information science offers new avenues for comprehending the information paradoxes involving black holes.
Heisenberg's uncertainty principle is a fundamental element in quantum mechanics. It sets a bound on our ability to predict the measurement outcomes of two incompatible observables simultaneously. In quantum information theory, the uncertainty principle can be expressed using entropic measures. The entropic uncertainty relation can be improved by considering an additional particle as a memory particle. The presence of quantum correlation between the memory particle and the measured particle reduces the uncertainty. In a curved space-time, the presence of the Hawking radiation can reduce quantum correlation. Therefore, concerning the relationship between the quantum correlation and entropic uncertainty lower bound, we expect that the Hawking radiation increases the entropic uncertainty lower bound. In this work, we investigate the entropic uncertainty relation in Garfinkle-Horowitz-Strominger (GHS) dilation black hole. We consider a model in which the memory particle is located near the event horizon outside the black hole, while the measured particle is free falling. To study the proposed model, we will consider examples with Dirac fields. We also explore the effect of the Hawking radiation on the quantum secret key rate.
Abstract The dynamical characteristics of measurement's uncertainty are investigated under two modes of Dirac field in the Garfinkle–Horowitz–Strominger dilation space‐time. It shows that the Hawking effect induced by the thermal field would result in an expansion of the entropic uncertainty with increasing dilation‐parameter value, as the systemic quantum coherence reduces, reflecting that the Hawking effect could undermine the systemic coherence. Meanwhile, the intrinsic relationship between the uncertainty and quantum coherence is obtained, and it is revealed that the uncertainty's bound is anti‐correlated with the system's quantum coherence. Furthermore, it is illustrated that the systemic mixedness is correlated with the uncertainty to a large extent. Via the information flow theory, various correlations including quantum and classical aspects, which can be used to form a physical explanation on the relationship between the uncertainty and quantum coherence, are also analyzed. Additionally, this investigation is extended to the case of multi‐component measurement, and the applications of the entropic uncertainty relation are illustrated on entanglement criterion and quantum channel capacity. Lastly, it is declared that the measurement uncertainty can be quantitatively suppressed through optimal quantum weak measurement. These investigations might pave an avenue to understand the measurement's uncertainty in the curved space‐time.
Abstract We investigate the quantum Fisher information (QFI) of a qubit-qutrit system in the background of Garfinkle–Horowitz–Strominger dilation black hole. After deriving the analytical expression of the QFI, we examine its dynamics with respect to the dilation parameter D and the state parameter γ of the system. Our results show that the QFI for the estimation of γ is a fixed value, which is independent of the parameters D and γ . And the QFI for the estimation of D varies with the parameters D and γ . Additionally, we propose an effective strategy to steer the QFI by introducing weak measurement reversal. We find that the QFI can be remarkably enhanced by adjusting the appropriate reversing measurement strengths. Our findings might provide some useful insights for the study on parameter estimation of hybrid systems in the framework of relativity theory.
We investigate the quantum correlation via measurement-induced-nonlocality (MIN) for Dirac particles in Garfinkle–Horowitz–Strominger (GHS) dilation space–time. It is shown that the physical accessible quantum correlation decreases as the dilation parameter increases monotonically. Unlike the case of scalar fields, the physical accessible correlation is not zero when the Hawking temperature is infinite owing to the Pauli exclusion principle and the differences between Fermi–Dirac and Bose–Einstein statistics. Meanwhile, the boundary of MIN related to Bell-violation is derived, which indicates that MIN is more general than quantum nonlocality captured by the violation of Bell-inequality. As a by-product, a tenable quantitative relation about MIN redistribution is obtained whatever the dilation parameter is. In addition, it is worth emphasizing that the underlying reason why the physical accessible correlation and mutual information decrease is that they are redistributed to the physical inaccessible regions.