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Annalen der Physik

Dynamical Measurement's Uncertainty in the Curved Space‐Time

Fei Ming, Dong Wang, Liu Ye

Published Jun 7, 2019• 39 citations
Publisher

Abstract

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.

DOI
10.1002/andp.201900014

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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 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.
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 Heisenberg uncertainty principle describes a basic restriction on an observer's ability of precisely predicting the measurement of a pair of noncommuting observables, and virtually is at the core of quantum mechanics. Herein, the aim is to study the entropic uncertainty relation (EUR) under the background of a Schwarzschild black hole and its control. Explicitly, dynamical features of the measuring uncertainty via entropy are developed in a practical model where a stationary particle interacts with its surrounding environment while another particle—serving as a quantum memory reservoir—undergoes free fall in the vicinity of the event horizon of the Schwarzschild space‐time. It shows higher Hawking temperatures would give rise to an inflation of the entropic uncertainty on the measured particle. This is suggestive of the fact the measurement uncertainty is strongly correlated with degree of mixing present in the evolving particles. Additionally, based on information flow theory, a physical interpretation for the observed dynamical behaviors related with the entropic uncertainty in such a genuine scenario is provided. Finally, an efficient strategy is proposed to reduce the uncertainty by non‐tracing‐preserved operations. Therefore, our explorations may improve the understanding of the dynamic entropic uncertainty in a curved space‐time, and illustrate predictions of quantum measurements in relativistic quantum information sciences.
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 The dynamic characteristics of measured uncertainty and quantum coherence are explored for an inertial Unruh–DeWitt detector model in an expanding de Sitter space. Using the entropic uncertainty relation, the uncertainty of interest is correlated with the evolving time t, the energy level spacing δ, and the Hubble parameter H. The investigation shows that, for short time, a strong energy level spacing and small Hubble parameter can result in a relatively small uncertainty. The evolution of quantum coherence versus the evolving time and Hubble parameter, which varies almost inversely to that of the uncertainty, is then discussed, and the relationship between uncertainty and the coherence is explicitly derived. With respect to the l1 norm of coherence, it is found that the environment for the quantum system considered possesses a strong non‐Markovian property. The dynamic behavior of coherence non‐monotonously decreases with the growth of evolving time. The dynamic features of uncertainty and coherence in the expanding space with those in flat space are also compared. Furthermore, quantum weak measurement is utilized to effectively reduce the magnitude of uncertainty, which offers realistic and important support for quantum precision measurements during the undertaking of quantum tasks.