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arXiv:2602.00991 · The European Physical Journal C

Tripartite quantum steering in Schwarzschild spacetime

Guang-Wei Mi, Xiaofen Huang, Tinggui Zhang

gr-qcquant-phSubmitted Feb 1, 2026• Announced Feb 3, 2026• 1 citation
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Abstract

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.

AI Summary

The paper studies how Hawking radiation affects directional steering across the three bipartitions of a generalized three-qubit GHZ state, $\alpha|000\rangle+\sqrt{1-\alpha^2}|111\rangle$, in Schwarzschild spacetime. Alice remains asymptotically far away, while Bob and Charlie are placed near the horizon. A standard fermionic Bogoliubov transformation introduces exterior particle and interior antiparticle modes, with Hawking temperature $T=1/(8\pi M)$. Tracing out different modes produces three-qubit X states containing three, two, or one exterior modes. Steering is detected through entanglement of auxiliary states obtained by adding local maximally mixed noise: the sufficient criteria use mixing parameters $1/\sqrt{3}$ for $1\rightarrow2$ steering and $1/3$ for $2\rightarrow1$ steering. Explicit inequalities yield normalized witness-based steering quantities for all six directions. Their temperature dependence is examined analytically and through plots at $\omega=1$ and $\alpha\in\{1/4,1/2,1/\sqrt{2}\}$. For the all-exterior subsystem, the reported steering quantities decrease with temperature; some $2\rightarrow1$ quantities vanish at finite temperature, while reciprocal quantities persist. Maximum asymmetry is reported at transitions classified as two-way to one-way steering. Subsystems containing interior modes exhibit increasing steering quantities, with nonmonotonic behavior in one direction and parameter-dependent onset thresholds. The treatment is restricted to this GHZ family and idealized field-mode description. Interior modes are explicitly acknowledged to be inaccessible to exterior observers. No dedicated limitations discussion is provided; importantly, the construction supplies sufficient steering witnesses, rather than necessary-and-sufficient tests establishing unsteerability when a witness vanishes.

Likely largely AI-generatedIncrementalOverclaimsPossible errorStrong assumptions

Central claim may not hold: The paper treats failure of sufficient steering witnesses as proof of unsteerability, so its asserted one-way regimes and exact two-way–to–one-way boundaries are not established. The formulas for AB→C and CA→B steering give different results for a state invariant under exchanging B and C, invalidating the claimed distinction between their disappearance behaviors. The five-mode state prints an excited-state contribution |11111⟩ where the stated mode transformation requires |11010⟩, although the subsequent reduced states correspond to the corrected term.

Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.

Journal reference
Eur. Phys. J. C (2026) 86:75
DOI
10.1140/epjc/s10052-025-15241-3
Comments
15pages, 3 figures

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The European Physical Journal C•Jul 29, 2026•0 citations
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.
The paper studies how Hawking radiation affects directional steering across the three bipartitions of a generalized three-qubit GHZ state, α∣000⟩+1−α2∣111⟩\alpha|000\rangle+\sqrt{1-\alpha^2}|111\rangleα∣000⟩+1−α2​∣111⟩, in Schwarzschild spacetime. Alice remains asymptotically far away, while Bob and Charlie are placed near the horizon. A standard fermionic Bogoliubov transformation introduces exterior particle and interior antiparticle modes, with Hawking temperature T=1/(8πM)T=1/(8\pi M)T=1/(8πM).
Tracing out different modes produces three-qubit X states containing three, two, or one exterior modes. Steering is detected through entanglement of auxiliary states obtained by adding local maximally mixed noise: the sufficient criteria use mixing parameters 1/31/\sqrt{3}1/3​ for 1→21\rightarrow21→2 steering and 1/31/31/3 for 2→12\rightarrow12→1 steering. Explicit inequalities yield normalized witness-based steering quantities for all six directions. Their temperature dependence is examined analytically and through plots at ω=1\omega=1ω=1 and α∈{1/4,1/2,1/2}\alpha\in\{1/4,1/2,1/\sqrt{2}\}α∈{1/4,1/2,1/2​}.
For the all-exterior subsystem, the reported steering quantities decrease with temperature; some 2→12\rightarrow12→1 quantities vanish at finite temperature, while reciprocal quantities persist. Maximum asymmetry is reported at transitions classified as two-way to one-way steering. Subsystems containing interior modes exhibit increasing steering quantities, with nonmonotonic behavior in one direction and parameter-dependent onset thresholds.
The treatment is restricted to this GHZ family and idealized field-mode description. Interior modes are explicitly acknowledged to be inaccessible to exterior observers. No dedicated limitations discussion is provided; importantly, the construction supplies sufficient steering witnesses, rather than necessary-and-sufficient tests establishing unsteerability when a witness vanishes.
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 study Gaussian quantum steering and its asymmetry in the background of a Schwarzschild black hole. We present a Gaussian channel description of quantum state evolution under the influence of Hawking radiation. We find that thermal noise introduced by the Hawking effect will destroy the steerability between an inertial observer Alice and an accelerated observer Bob who hovers outside the event horizon, while it generates steerability between Bob and a hypothetical observer anti-Bob inside the event horizon. Unlike entanglement behaviors in curved spacetime, here the steering from Alice to Bob suffers from a ``sudden death'' and the steering from anti-Bob to Bob experiences a ``sudden birth'' with increasing Hawking temperature. We also find that the Gaussian steering is always asymmetric and the maximum steering asymmetry cannot exceed ln2\mathrm{ln}2ln2, which means the state never evolves to an extremal asymmetry state. Furthermore, we obtain the parameter settings that maximize steering asymmetry and find that (i) $s=\mathrm{arccosh}\frac{{\mathrm{cosh}}^{2}r}{1\ensuremath{-}{\mathrm{sinh}}^{2}r}$ is the critical point of steering asymmetry and (ii) the attainment of maximal steering asymmetry indicates the transition between one-way steerability and both-way steerability for the two-mode Gaussian state under the influence of Hawking radiation.
We systematically investigate the directional dependence of Gaussian quadripartite quantum steering and its redistribution among different modes in the background of a Schwarzschild black hole. For physically accessible sectors, we identify three distinct behaviors: (i) steering from non-gravitational to gravitational observers undergoes sudden death at maximal asymmetry with the Hawking temperature, marking the crossover from two-way to one-way steerability; (ii) steering in the opposite direction decays monotonically and vanishes only in the extreme black hole limit, highlighting its directional sensitivity to spacetime curvature; (iii) steering from hybrid gravitational-non-gravitational partitions to non-gravitational mode persists at a finite asymptotic value set by the initial squeezing parameter. Moreover, all inaccessible steerings generated by the Hawking effect exhibit an intrinsic asymmetry, with their specific behavior being strongly dependent on the steering direction.
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.
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.