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arXiv:2511.01561 · Physics Letters B

Does the survival and sudden death of quadripartite steering in curved spacetime truly depend on multi-directionality?

Xiaobao Liu, Wentao Liu, Si-Han Shang, Shu-Min Wu

gr-qcquant-phSubmitted Nov 3, 2025• Announced Nov 4, 2025• 0 citations
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Abstract

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.

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23 pages, 3 figures

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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.
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 investigate the redistribution and directional properties of Gaussian tripartite quantum steering in de-Sitter space within the continuous-variable framework. By expressing the Bunch-Davies vacuum in terms of the open-chart modes through a Bogoliubov transformation, we derive the covariance matrix of the resulting multipartite Gaussian state and analyze both one-to-two and two-to-one steering configurations. We find that de-Sitter curvature generally suppresses the steering initially shared among the accessible modes, but its influence depends strongly on the steering direction. In particular, while some steering configurations undergo sudden death at finite curvature, two-to-one steering toward a nongravitational mode remains finite throughout the parameter range considered, demonstrating a robustness of tripartite steering absent in its bipartite counterpart. Remarkably, the maximum steering asymmetry occurs at the critical point at which steering in one direction undergoes sudden death, marking the transition from two-way to one-way steering. We further show that the de-Sitter gravitational field can generate tripartite steering involving modes separated by the cosmological horizon. Depending on the steering partition, this curvature-induced steering exhibits persistent one-way or asymmetric two-way behavior, as well as a sudden-birth transition from one-way to two-way steering. These results demonstrate that de-Sitter curvature not only degrades preexisting quantum correlations but also redistributes and generates directional multipartite steering across causally disconnected regions.
In a relativistic framework, it is generally accepted that quantum steering of maximally entangled states provides greater advantages in practical applications compared to non-maximally entangled states. In this paper, we investigate quantum steering for four different types of Bell-like states of fermionic modes near the event horizon of a Schwarzschild black hole. In some parameter spaces, the peak of steering asymmetry corresponds to a transition from two-way to one-way steerability for Bell-like states under the influence of the Hawking effect. It is intriguing to find that the fermionic steerability of the maximally entangled states experiences sudden death with the Hawking temperature, while the fermionic steerability of the non-maximally entangled states maintains indefinite persistence at infinite Hawking temperature. In contrast to prior research, this finding suggests that quantum steering of non-maximally entangled states is more advantageous than that of maximally entangled states for processing quantum tasks in the gravitational background. This surprising result overturns the traditional idea of “the advantage of maximally entangled steering in the relativistic framework” and provides a new perspective for understanding the Hawking effect 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.
Abstract We study Gaussian quantum steering in the Schwarzschild–de Sitter (SdS) spacetime that is endowed with both a black hole event horizon (BEH) and a cosmological event horizon (CEH), giving rise to two different Hawking temperatures. It is shown that the Hawking effect of the black hole always reduces the quantum steering, but the Hawking effect of the expanding universe does not always play the same role. For the first time, we find that the Hawking effect can improve quantum steering. We also find that the observer who locates in the BEH has stronger steerability than the observer who locates in CEH. Further, we study the steering asymmetry, and the conditions for two-way, one-way and no-way steering in the SdS spacetime. Finally, we study the Gaussian quantum steering in the scenario of effective equilibrium temperature. We show that quantum steering reduces monotonically with the effective temperature but now increases monotonically with the Hawking temperature of the black hole, which banishes the belief that the Hawking effect can only destroy quantum steering.