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arXiv:2609.00485

Dynamical evolution of quantum mutual information in Schwarzschild spacetime

Guosen Ma, Fang Rao, Jingjing Hua, Xiaofen Huang

Published Aug 31, 2026• 0 citations
arXivHTMLPDF

Abstract

Quantum mutual information is a fundamental quantity for characterizing correlations among quantum systems. In this work, we investigate the dynamic evolution of the quantum mutual information based on Rényi-2 entropy for three-mode Gaussian states in the background of a Schwarzschild black hole. We find that the physically inaccessible mutual information increases with Hawking temperature and eventually saturates, while the physically accessible mutual information exhibits nonmonotonic temperature dependence: it first rises, reaches a peak, then declines toward a finite asymptotic value. This nonmonotonic behavior differs from the monotonic degradation typically observed for Gaussian entanglement and steering in curved spacetime. Furthermore, we establish several constraint relations governing the distribution of mutual information among subsystems. These findings contribute to understanding the quantumness of quantum correlations for continuous variable in Schwarzschild spacetime.

DOI
10.48550/arxiv.2609.00485

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Quantum mutual information is a fundamental quantity for characterizing correlations among quantum systems. In this work, we investigate the dynamic evolution of the quantum mutual information based on Rényi-2 entropy for three-mode Gaussian states in the background of a Schwarzschild black hole. We find that the physically inaccessible mutual information increases with Hawking temperature and eventually saturates, while the physically accessible mutual information exhibits nonmonotonic temperature dependence: it first rises, reaches a peak, then declines toward a finite asymptotic value. This nonmonotonic behavior differs from the monotonic degradation typically observed for Gaussian entanglement and steering in curved spacetime. Furthermore, we establish several constraint relations governing the distribution of mutual information among subsystems. These findings contribute to understanding the quantumness of quantum correlations for continuous variable in Schwarzschild spacetime.
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.
Abstract In the past two decades, the exploration of quantumness within Schwarzschild spacetime has garnered significant interest, particularly regarding the Hawking radiation’s impact on quantum correlations and quantum coherence. Building on this foundation, we investigate how Hawking radiation influences maximal steered coherence (MSC)-a crucial measure for gauging the ability to generate coherence through steering. We find that as the Hawking temperature increases, the physically accessible MSC degrade while the unaccessible MSC increase. This observation is attributed to a redistribution of the initial quantum correlations, previously acknowledged by inertial observers, across all bipartite modes. In particular, we find that in limit case that the Hawking temperature tends to infinity, the accessible MSC equals to 1/21/\sqrt{2}1/2​ 1 / 2 of its initial value, and the unaccessible MSC between mode A and B‾\overline{B}B B ¯ also equals to the same value. Our findings illuminate the intricate dynamics of quantum information in the vicinity of black holes, suggesting that Hawking radiation plays a pivotal role in reshaping the landscape of quantum coherence and entanglement in curved spacetime. This study not only advances our theoretical understanding of black hole thermodynamics but also opens new avenues for investigating the interface between quantum mechanics and general relativity.
The effect of Hawking radiation on the redistribution of the entanglement and mutual information in the Schwarzschild spacetime is investigated. Our analysis shows that the physically accessible correlations degrade while the unaccessible correlations increase as the Hawking temperature increases because the initial correlations described by inertial observers are redistributed between all the bipartite modes. It is interesting to note that, in the limit case that the temperature tends to infinity, the accessible mutual information equals to just half of its initial value, and the unaccessible mutual information between mode A and II also equals to the same value.
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.
To characterize the effect of Hawking radiation induced by the quantum atmosphere beyond the event horizon on entanglement, we employ concurrence as the entanglement measure for a bipartite mixed state and investigate its evolution with Hawking temperature. We find that the physically accessible concurrence decreases as the Hawking acceleration increases, whereas the physically inaccessible concurrence exhibits the opposite behavior, increasing monotonically from zero. We further establish several trade-off relations on concurrence, revealing its distribution between physically accessible and inaccessible regions. Additionally, we study the dynamics of concurrence under three types of channel noise. The results indicate that the evolution of concurrence depends on the specific noise channel: unlike the phase damping channel, sudden death of concurrence occurs in both phase flip and bit flip channels, the concurrence exhibits a certain symmetry with respect to the noise parameter during its evolution under bit flip channel noise.
Abstract The black hole information paradox arises from the tension between the thermal spectral properties of Hawking radiation and the unitarity principle in quantum mechanics. To explore the dynamical evolution characteristics of quantum fields in this context, we employ the standard quantization formalism for Dirac fields in Schwarzschild spacetime and investigate the coupling structure of particle and antiparticle modes within a framework that transcends the single-mode approximation. By calculating the states of externally observable subsystems, we systematically derive the evolution of concurrence and first-order coherence as functions of the Hawking temperature. Additionally, we assess the impact of varying initial parameters on these quantities. We further contrast the quantum entanglement differences between the observable exterior region and the black hole interior across diverse temperature regimes. These results provide valuable insights into the evolution of entanglement and coherence in curved spacetime.