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Laser Physics Letters

Uncertainty relations for quantum coherence in the background of dilaton black holes

Xiao‐Gang Fan, Zhiyong Ding, Huan Yang, Juan He, Liu Ye

Published Jun 25, 2019• 9 citations
Publisher

Abstract

Abstract The coherence of a quantum system can be considered as the available physical resource, and its quantification respects the choice of reference bases. In this paper, we propose the uncertainty relations for quantum coherence (URQC) of a bipartite system AB in mutually unbiased bases, where particle A is the measured particle and B is regarded as the quantum memory. It is confirmed that the Holevo quantity can improve the lower bound of coherence. By defining the tightness as the difference between coherence and its lower bound, we find that the tightness of the improved URQC is independent of the quantum memory. As an example of application, we investigate the URQC of Dirac particles in the background of a Garfinkle–Horowitz–Strominger dilaton black hole beyond the single-mode approximation. It shows that the lower bound of coherence decreases monotonically with the increase of dilaton parameter due to the Hawking effect. Moreover, since the subsystem A is not affected by the black hole, the tightness of the improved URQC is always keep constant. It worth mentioning that the change of coherence can be precisely predicted via the known tightness and the improved lower bound measured experimentally.

DOI
10.1088/1612-202x/ab2232

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Abstract The coherence of a quantum system can be considered as the available physical resource, and its quantification respects the choice of reference bases. In this paper, we propose the uncertainty relations for quantum coherence (URQC) of a bipartite system AB in mutually unbiased bases, where particle A is the measured particle and B is regarded as the quantum memory. It is confirmed that the Holevo quantity can improve the lower bound of coherence. By defining the tightness as the difference between coherence and its lower bound, we find that the tightness of the improved URQC is independent of the quantum memory. As an example of application, we investigate the URQC of Dirac particles in the background of a Garfinkle–Horowitz–Strominger dilaton black hole beyond the single-mode approximation. It shows that the lower bound of coherence decreases monotonically with the increase of dilaton parameter due to the Hawking effect. Moreover, since the subsystem A is not affected by the black hole, the tightness of the improved URQC is always keep constant. It worth mentioning that the change of coherence can be precisely predicted via the known tightness and the improved lower bound measured experimentally.
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.
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 investigate the nonseparability of N-partite quantum systems by employing the Abe-Rajagopal (AR) q -conditional entropy for both free bosonic and fermionic fields in the background of a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. An intriguing finding is that the Hawking effect of the black hole can generate a net nonseparability of W state for fermionic field. Notably, we observe that fermionic nonseparability exhibits a stronger robustness than its bosonic counterpart, while fermionic coherence is found to be weaker than bosonic coherence within the dilaton black hole background. Additionally, our analysis reveals that the nonseparability of GHZ state is more pronounced than that of W state, yet quantum coherence of GHZ state is comparatively weaker than that of W state in dilaton spacetime. These results suggest that choosing the appropriate quantum resources for different particle types and quantum state configurations is essential for effectively tackling relativistic quantum information tasks.
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.
For a pair of incompatible quantum measurements, the total uncertainty can be bounded by a state-independent constant. However, such a bound can be violated if the quantum system is entangled with another quantum system (called memory); the quantum correlation between the systems can reduce the measurement uncertainty. On the other hand, in a curved spacetime, the presence of the Hawking radiation can reduce quantum correlation. The interplay of quantum correlation in the curved spacetime has become an interesting arena for studying uncertainty relations. Here we demonstrate that the bounds of the entropic uncertainty relations, in the presence of memory, can be formulated in terms of the Holevo quantity, which limits how much information can be encoded in a quantum system. Specifically, we considered examples with Dirac fields with and without spin, near the event horizon of a Schwarzschild black hole, the Holevo bound provides a better bound than the previous bound based on the mutual information. Furthermore, as the memory moves away from the black hole, the difference between the total uncertainty and the new lower bound remains a constant, not depending on any property of the black hole.
Abstract We study the dynamics of Gaussian quantum coherence under the background of a Garfinkle–Horowitz–Strominger dilaton black hole. It is shown that the dilaton field has evident effects on the degree of coherence for all the bipartite subsystems. The bipartite Gaussian coherence is not affected by the frequency of the scalar field for an uncharged or an extreme dilaton black hole. It is found that the initial coherence is not completely destroyed even for an extreme dilaton black hole, which is quite different from the behavior of quantum steering because the latter suffers from a “sudden death” under the same conditions. This is nontrivial because one can employ quantum coherence as a resource for quantum information processing tasks even if quantum correlations have been destroyed by the strong gravitational field. In addition, it is demonstrated that the generation of quantum coherence between the initial separable modes is easier for low-frequency scalar fields. At the same time, quantum coherence is smoothly generated betweenone pair of partners and exhibits a “sudden birth” behavior between another pairs in the curved spacetime.