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Annalen der Physik

Tripartite Uncertainty, Quantum, and Classical Correlations Dynamics under Unruh Effect

A.‐B. A. Mohamed, Ahmad N. Khedr, S. M. Younis

Published May 8, 2023• 5 citations
Publisher

Abstract

Abstract How the dynamics of classical and quantum correlations due to the Unruh effect are reflected in the properties of tripartite entropic uncertainty is investigated. It is found that, despite the quantum correlations disappearing at the limit of infinite acceleration, the uncertainty about the measurement outcome is at its minimum. This is due to the three‐qubit system still containing classic correlations at that stage of acceleration. Additionally, the decrease in the entropic uncertainty when the measured qubit interacts strongly with the scalar field can be attributed to the increase in classical correlations. Furthermore, it is found that the entropic uncertainty is fully anti‐correlated to classical correlations, and minimal uncertainty can be obtained even in the absence of quantum correlations. A tremendously tight constraint that effectively defined the properties of tripartite entropic uncertainty based on the difference between the total correlation and the Holevo quantities is achieved.

DOI
10.1002/andp.202300001

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Abstract How the dynamics of classical and quantum correlations due to the Unruh effect are reflected in the properties of tripartite entropic uncertainty is investigated. It is found that, despite the quantum correlations disappearing at the limit of infinite acceleration, the uncertainty about the measurement outcome is at its minimum. This is due to the three‐qubit system still containing classic correlations at that stage of acceleration. Additionally, the decrease in the entropic uncertainty when the measured qubit interacts strongly with the scalar field can be attributed to the increase in classical correlations. Furthermore, it is found that the entropic uncertainty is fully anti‐correlated to classical correlations, and minimal uncertainty can be obtained even in the absence of quantum correlations. A tremendously tight constraint that effectively defined the properties of tripartite entropic uncertainty based on the difference between the total correlation and the Holevo quantities is achieved.
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.
Quantum uncertainty is deeply linked to quantum correlations and relativistic motion. The entropic uncertainty relation with quantum memory offers a powerful way to study how shared entanglement affects measurement precision. However, under acceleration, the Unruh effect can degrade quantum correlations, raising questions about the reliability of QMA-EUR in such settings. Here, we investigate the QMA-EUR for two uniformly accelerating Unruh-DeWitt detectors coupled to a massless scalar field. Using the Kossakowski-Lindblad master equation, we calculate the entropic uncertainty, its lower bound, and the tightness of the relation under different Unruh temperatures. We find that acceleration does not always increase the lower bound on the uncertainty relation. Depending on the initial correlations between the detectors, it may either increase or decrease. This behavior results from the interplay between quantum discord and minimal missing information. Interestingly, a higher quantum discord does not necessarily lead to lower uncertainty.
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 The uncertainty principle offers a bound to show accuracy of the simultaneous measurement outcome for two incompatible observables. In this letter, we investigate quantum-memory-assisted entropic uncertainty relation (QMA–EUR) when the particle to be measured stays at an open system, and another particle is treated as quantum memory under a noninertial frame. In such a scenario, the collective influence of the unital and nonunital noise environment, and of the relativistic motion of the system, on the QMA–EUR is examined. By numerical analysis, we conclude that, firstly, the noises and the Unruh effect can both increase the uncertainty, due to the decoherence of the bipartite system induced by the noise or Unruh effect; secondly, the uncertainty is more affected by the noises than by the Unruh effect from the acceleration; thirdly, unital noises can reduce the uncertainty in long-time regime. We give a possible physical interpretation for those results: that the information of interest is redistributed among the bipartite, the noisy environment and the physically inaccessible region in the noninertial frame. Therefore, we claim that our observations provide an insight into dynamics of the entropic uncertainty in a noninertial frame, and might be important to quantum precision measurement under relativistic motion.
The uncertainty principle is a remarkable and fundamental feature in quantum mechanics that suggests a significant lower bound to predict the results of arbitrary incompatible observables measured on a particle. In this work, we study the dynamics of a tripartite entropic uncertainty bound and quantum fidelity in a three non-interacting qubits model initially prepared in a maximally entangled pure Greenberger–Horne–Zeilinger state and then subjected to classical environmental noise in different and common environments. Interestingly, we find that the dynamics of the tripartite uncertainty bound and fidelity are strongly affected by the type of system–environment interaction, and the growth speed of the uncertainty bound is strongly influenced by the disorder of the environment. Explicitly, our results show that the uncertainty bound and fidelity can be improved when the qubits are coupled to the noise in a common environment.
Abstract We study the acceleration effect on the genuine tripartite entanglement for one or two accelerated detector(s) coupled to the vacuum field. Surprisingly, we find that the increase and decrease in entanglement have no definite correspondence with the Unruh and anti-Unruh effects. Specifically, Unruh effect can not only decrease but also enhance the tripartite entanglement between detectors; also, anti-Unruh effect can not only enhance but also decrease the tripartite entanglement. We give an explanation of this phenomenon. Finally, we extend the discussion from tripartite to N-partite systems.