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Annalen der Physik

Quantum Steering of Imaginarity in Schwarzschild Spacetime

Bing Yu, Xiaoyong Yang, Xiaoli Hu, Zhi‐Xiang Jin, Xiaofen Huang

Published Aug 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT We study the distribution of quantum imaginarity in Schwarzschild spacetime under Hawking radiation via imaginarity steering functionals. For bipartite systems, we analyze Werner states and general two‐qubit X‐states and find that the steering functional of physically accessible states decreases monotonically with Hawking temperature, shrinking the steerable region, whereas physically inaccessible states remain unsteerable for all temperatures. For multipartite systems, we consider general three‐qubit pure states up to local unitary equivalence and show that Hawking radiation induces a family of monogamy‐like steering inequalities with temperature‐independent bounds determined by subsystem accessibility. The corresponding maximal sum of imaginarity steering functionals decreases as the Hawking temperature increases when both subsystems are accessible, remains invariant when only one subsystem is inaccessible, and increases when both subsystems are inaccessible. These results reveal how Hawking radiation reshapes the distribution of imaginarity in relativistic spacetime.

DOI
10.1002/andp.70267

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gr-qcCross-listedarXiv:2602.00991•The European Physical Journal C•Feb 3, 2026•1 citation
ABSTRACT We study the distribution of quantum imaginarity in Schwarzschild spacetime under Hawking radiation via imaginarity steering functionals. For bipartite systems, we analyze Werner states and general two‐qubit X‐states and find that the steering functional of physically accessible states decreases monotonically with Hawking temperature, shrinking the steerable region, whereas physically inaccessible states remain unsteerable for all temperatures. For multipartite systems, we consider general three‐qubit pure states up to local unitary equivalence and show that Hawking radiation induces a family of monogamy‐like steering inequalities with temperature‐independent bounds determined by subsystem accessibility. The corresponding maximal sum of imaginarity steering functionals decreases as the Hawking temperature increases when both subsystems are accessible, remains invariant when only one subsystem is inaccessible, and increases when both subsystems are inaccessible. These results reveal how Hawking radiation reshapes the distribution of imaginarity in relativistic spacetime.
Black hole spacetimes provide a natural setting for quantum systems in curved spacetime, where effects such as Hawking radiation arise from event horizons. In this work, we investigate the impact of the Hawking effect on quantum imaginarity in Schwarzschild spacetime, focusing on nonlocal advantage of quantum imaginarity (NAQI) and assisted imaginarity distillation. For NAQI, it is significantly affected by Hawking radiation, exhibiting a pronounced difference between physically accessible and inaccessible regions. It is suppressed in the physically accessible region with increasing Hawking temperature and may vanish, while remaining absent in the physically inaccessible region across the parameter regime. For assisted imaginarity distillation, the Hawking effect modifies the assisted fidelity in a state-dependent manner. In the physically accessible region, the fidelity generally decreases with increasing temperature, indicating reduced distillation capability, whereas the physically inaccessible region exhibits the opposite monotonic trend, indicating enhanced distillation capability. These results highlight distinct operational behaviors of physically accessible and inaccessible regions under relativistic effects, providing insight into quantum imaginarity in curved spacetime.
Abstract Using two different types of quantification for quantum steering, we study the influence of Hawking radiation on quantum steering for fermionic fields in Schwarzschild spacetime. The degradation for the steering between physically accessible observers and the generation for the steering between physically accessible and inaccessible observers induced by Hawking radiation are studied. We also reveal the difference between the two types of quantification for steering, and find some monogamy relations between steering and entanglement. Furthermore, we show the different properties between fermionic steering and bosonic steering in Schwarzschild 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.
Quantum imaginarity, as a critical resource metric for quantifying intrinsic nonreal coherence encoded in quantum states, exhibits nontrivial evolutionary behaviors in curved spacetime backgrounds. This work focuses on bipartite Dirac field reduced states in the quantum atmosphere of a static Schwarzschild black hole, aiming to explore the modulation of three mainstream imaginarity measures by Hawking thermal radiation. We reveal that the relative-entropy imaginarity, the geometric imaginarity and robustness of imaginarity, the fully accessible state presents a valley-shaped radial profile with a local minimum inside the quantum atmosphere, while the cross-coupling and fully inaccessible states follow opposite peak-shaped trends. Further analysis demonstrates that the Hartle-Hawking constant significantly strengthens the redistribution effect of imaginarity across both regions, whereas an increase in the event horizon radius weakens such redistribution and flattens the extremum features. These findings offer a new perspective for decoding the information structure of black hole quantum atmospheres and the intrinsic quantum nature of Hawking radiation.
Multipartite steering is a fundamental quantum resource that is uniquely suited to tackling complex relativistic quantum information challenges, but its properties in the gravitational field context remain to be elucidated. We study the distribution of Gaussian tripartite steering in the background of a Schwarzschild black hole. Our results show that physically accessible 2 → 1 steerability remains robust at any Hawking temperature, which contrasts with the behavior of 1 → 1 steering that experiences “sudden death” as the Hawking temperature increases, making 2 → 1 steerability a more reliable candidate for relativistic quantum information tasks. Notably, we observe that the sudden death of quantum steering is accompanied by a peak in steering asymmetry, signifying a critical transition from two-way steering to one-way steering in the relativistic three-mode system. We find that the Hawking effect can generate inaccessible two-way steering of a bipartite system in both directions, as shown in Wang et al. (2016) [73] , while it can only generate physically inaccessible one-way 2 → 1 steering in tripartite systems. These insights enhance our understanding of the redistribution of multipartite steering near the event horizon of the black hole.
We investigate the effects of Hawking radiation on quantum steering and steering asymmetry in a tripartite system embedded in Schwarzschild spacetime. All tripartite steering types were classified,comprising three "1 to 2" and three "2 to 1" steering cases. Through a systematic analysis of all physically relevant scenarios (including accessible and inaccessible modes), we classify three canonical scenarios with one, two and three physically accessible modes. In the scenario of three physically accessible modes, Hawking radiation disrupts quantum steering, with the maximum steering asymmetry during the two-way steering to one-way steering transition precisely demarcating the phase boundary between these regimes. For two physically accessible modes, Hawking radiation exhibits dual behavior: enhancing the steering from Alice and Bob to anti-Charlie under certain parameters while suppressing it under others, while net strengthening other steering types. When considering one physically accessible mode, the Hawking effect of the black hole significantly enhances quantum steering. These findings provide new insights into quantum correlations in curved spacetime and establish observable signatures of Hawking effects in quantum steering phenomena.