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arXiv:2408.07789 · The European Physical Journal C

Tripartite measurement uncertainty in Schwarzschild space-time

Hazhir Dolatkhah, Artur Czerwiński, Asad Ali, Saif M. Al-Kuwari, Saeed Haddadi

Published Nov 18, 2024• 12 citations
arXivHTMLPDF

Abstract

Abstract The effect of Hawking radiation on tripartite measurement uncertainty in a Schwarzschild black hole background is analyzed in this study. Two scenarios are examined. In the first, quantum memory particles approach a Schwarzschild black hole and are positioned near the event horizon, while the particle being measured remains in the asymptotically flat region. In the second scenario, the measured particle moves toward the black hole, and the quantum memories stay in the asymptotically flat region. This study considers two initial quantum states, namely GHZ and W states. Our findings reveal that in both cases, measurement uncertainty increases steadily with rising Hawking temperature. When comparing the GHZ and W states, the GHZ state initially exhibits lower measurement uncertainty at low Hawking temperatures than the W state, indicating greater resilience to Hawking radiation. Additionally, when the quantum memories remain in the asymptotically flat region while the measured particle falls toward the black hole, the uncertainties for GHZ and W states do not align at high temperatures. The GHZ state consistently demonstrates lower measurement uncertainty, showcasing its superior robustness against Hawking radiation.

DOI
10.1140/epjc/s10052-024-13554-3

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Abstract The effect of Hawking radiation on tripartite measurement uncertainty in a Schwarzschild black hole background is analyzed in this study. Two scenarios are examined. In the first, quantum memory particles approach a Schwarzschild black hole and are positioned near the event horizon, while the particle being measured remains in the asymptotically flat region. In the second scenario, the measured particle moves toward the black hole, and the quantum memories stay in the asymptotically flat region. This study considers two initial quantum states, namely GHZ and W states. Our findings reveal that in both cases, measurement uncertainty increases steadily with rising Hawking temperature. When comparing the GHZ and W states, the GHZ state initially exhibits lower measurement uncertainty at low Hawking temperatures than the W state, indicating greater resilience to Hawking radiation. Additionally, when the quantum memories remain in the asymptotically flat region while the measured particle falls toward the black hole, the uncertainties for GHZ and W states do not align at high temperatures. The GHZ state consistently demonstrates lower measurement uncertainty, showcasing its superior robustness against Hawking radiation.
Abstract We investigate tripartite quantum-memory-assisted entropic uncertain and quantum coherence for GHZ and W states of a fermionic field in the background of a spherically symmetric black hole of Einstein–Gauss–Bonnet (EGB) gravity. Two distinct scenarios are analyzed: (i) the quantum memories (held by Bob and Charlie) are near the horizon while the measured particle (Alice) remains in the flat region, and (ii) the reverse configuration. Dimensional dependence is observed: in d>5d>5d>5 d > 5 dimensions, the measurement uncertainty decreases monotonically with increasing horizon radius, while coherence increases; in d=5d=5d=5 d = 5 , both quantities exhibit non-monotonic behavior due to distinctive thermodynamic properties. Furthermore, comparative analysis reveals that the W state exhibits higher robustness in preserving coherence, whereas the GHZ state shows greater resistance to measurement uncertainty increase induced by Hawking radiation. Notably, the two scenarios yield qualitatively distinct behaviors: quantum coherence is consistently lower in Scenario 1 (quantum memory near horizon) than in Scenario 2 (measured particle near horizon), irrespective of the quantum state. For measurement uncertainty, the W state displays lower uncertainty in Scenario 1, while the GHZ state exhibits the opposite trend, with higher measurement uncertainty in Scenario 1. These results indicate that the characteristics of different quantum resources provide important insights into the selection and optimization of quantum states for information processing in curved spacetime.
Abstract The merging of quantum information science with the relativity theory presents novel opportunities for understanding the enigmas surrounding the transmission of information in relation to black holes. For this purpose, we study the quantumness near a Schwarzschild black hole in a practical model under decoherence. The scenario we consider in this paper is that a stationary particle in the flat region interacts with its surroundings while another particle experiences free fall in the vicinity of a Schwarzschild black hole’s event horizon. We explore the impacts of Hawking radiation and decoherence on the system under investigation and find that these effects can limit the survival of quantum characteristics, but cannot destroy them completely. Hence, the results of this study possess the potential to yield valuable insights into the comprehension of the quantum properties of a real system operating within a curved space-time framework.
We explore the entropic uncertainty relation in the curved background outside a Schwarzschild black hole , and find that Hawking radiation introduces a nontrivial modification on the uncertainty bound for particular observer, therefore it could be witnessed by proper uncertainty game experimentally. We first investigate an uncertainty game between a free falling observer and his static partner holding a quantum memory initially entangled with the quantum system to be measured. Due to the information loss from Hawking decoherence, we find an inevitable increase of the uncertainty on the outcome of measurements in the view of static observer, which is dependent on the mass of the black hole, the distance of observer from event horizon , and the mode frequency of quantum memory. To illustrate the generality of this paradigm, we relate the entropic uncertainty bound with other uncertainty probe, e.g., time–energy uncertainty. In an alternative game between two static players, we show that quantum information of qubit can be transferred to quantum memory through a bath of fluctuating quantum fields outside the black hole. For a particular choice of initial state, we show that the Hawking decoherence cannot counteract entanglement generation after the dynamical evolution of system, which triggers an effectively reduced uncertainty bound that violates the intrinsic limit − log 2 ⁡ c . Numerically estimation for a proper choice of initial state shows that our result is comparable with possible real experiments. Finally, a discussion on the black hole firewall paradox in the context of entropic uncertainty relation is given.
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.
In this paper, the effect of Hawking radiation on the multipartite entanglement of Dirac particles in the background of a Schwarzschild black hole is investigated. It is shown that all the 1-tangles decrease as the Hawking temperature grows, and the Coffman--Kundu--Wootters monogamy inequality is always saturated in this system. It is also shown that the entanglement's status of subsystems, which have the same quantum state, depend on its detector's position, and this proposition can be generalized to a multipartite system. Then, we find that the Hawking effect does not change the entanglement structure of the quantum state in Schwarzschild space-time. In addition, we discuss the distributions of quantum information and find that not only is the entanglement redistributed, but also the mutual information is distributed to the physical inaccessible region. At last, we calculate the mutual information of a NNN-qubit multipartite system, ${|\mathrm{\ensuremath{\Psi}}⟩}_{123\dots{}N}={(\ensuremath{\beta}{|0⟩}^{\ensuremath{\bigotimes}N}+\sqrt{1\ensuremath{-}{\ensuremath{\beta}}^{2}}{|1⟩}^{\ensuremath{\bigotimes}N})}_{123\dots{}N}$, and draw a conclusion that when the black hole approximates to evaporate completely the mutual information of this system will be close to $(N\ensuremath{-}1)/N$ of the original if a particle freely falls in toward a Schwarzschild black hole and locates near the event horizon, and the other particles remain in the asymptotically flat region.
Abstract We investigate the behavior of quantum correlations and quantum uncertainty in tripartite systems subjected to Hawking radiation in the background of a Schwarzschild black hole. By considering different bipartitions of accessible and inaccessible field modes separated by the event horizon, we analyze three complementary quantum information measures: the symmetry resolved entanglement entropy (SREE), the quantum speed limit (QSL), and the Wigner Yanase Skew information (SI). Our analysis shows that the QSL decreases monotonically with increasing Hawking temperature, indicating that Hawking radiation enhances the distinguishability of the reduced quantum states along the Hawking radiation trajectory. In contrast, the skew information decreases only for partitions composed solely of accessible modes, reflecting a reduction in local quantum uncertainty caused by thermal mixing. The SREE, however, decreases only when the subsystem includes the inaccessible inside horizon mode of Alice, revealing a suppression of symmetry sector mixing due to the redistribution of entanglement across the horizon. These results demonstrate that Hawking radiation does not simply degrade quantum correlations but instead redistributes them between accessible and inaccessible sectors of the field. The combined analysis of SREE, SI, and QSL therefore provides a unified perspective on how relativistic effects reshape quantum information in curved spacetime.