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arXiv:1710.04409 · Annalen der Physik

Monogamy of Einstein‐Podolsky‐Rosen Steering in the Background of an Asymptotically Flat Black Hole

Jieci Wang, Jiliang Jing, Heng Fan

Published Nov 14, 2017• 17 citations
arXivHTMLPDF

Abstract

Abstract We study the behavior of monogamy deficit and monogamy asymmetry for Einstein‐Podolsky‐Rosen steering of Gaussian states under the influence of the Hawking effect. We demonstrate that the monogamy of quantum steering shows an extreme scenario in the curved spacetime: the first part of a tripartite system cannot individually steer two other parties, but it can steer the collectivity of the remaining two parties. We also find that the monogamy deficit of Gaussian steering, a quantifier of genuine tripartite steering, are generated due to the influence of the Hawking thermal bath. Our results elucidate the structure of quantum steering in tripartite quantum systems in curved spacetime.

DOI
10.1002/andp.201700261

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Abstract We study the redistribution of quantum steering and its monogamy in the presence of a four-dimensional Kerr-Newman black hole. The gravitational effect of the Kerr-Newman black hole is shown to generate genuine tripartite steering between causally disconnected regions, depending on the polar angle, angular momentum, electric charge, and magnetic charge of the black hole. We obtain strong evidence of steering monogamy, that is, the "sudden death" of the A → B steering results in the "sudden birth" of B → B steering. We also obtain the condition of maximal steering asymmetry, that is, , revealing the transition between two-way and one-way steering in Kerr-Newman spacetime.

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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.

gr-qcCross-listedarXiv:2511.01561•Physics Letters B•Nov 4, 2025•0 citations
Abstract We study the behavior of monogamy deficit and monogamy asymmetry for Einstein‐Podolsky‐Rosen steering of Gaussian states under the influence of the Hawking effect. We demonstrate that the monogamy of quantum steering shows an extreme scenario in the curved spacetime: the first part of a tripartite system cannot individually steer two other parties, but it can steer the collectivity of the remaining two parties. We also find that the monogamy deficit of Gaussian steering, a quantifier of genuine tripartite steering, are generated due to the influence of the Hawking thermal bath. Our results elucidate the structure of quantum steering in tripartite quantum systems in curved spacetime.
Abstract We study the redistribution of quantum steering and its monogamy in the presence of a four-dimensional Kerr-Newman black hole. The gravitational effect of the Kerr-Newman black hole is shown to generate genuine tripartite steering between causally disconnected regions, depending on the polar angle, angular momentum, electric charge, and magnetic charge of the black hole. We obtain strong evidence of steering monogamy, that is, the "sudden death" of the A → B steering results in the "sudden birth" of B → B steering. We also obtain the condition of maximal steering asymmetry, that is, , revealing the transition between two-way and one-way steering in Kerr-Newman spacetime.
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 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.
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.
Monogamy inequalities for the way bipartite Einstein-Podolsky-Rosen (EPR) steering can be distributed among NNN systems are derived. One set of inequalities is based on witnesses with two measurement settings, and may be used to demonstrate correlation of outcomes between two parties, that cannot be shared with more parties. It is shown that the monogamy for steering is directional. Two parties cannot independently demonstrate steering of a third system, using the same two-setting steering witness, but it is possible for one party to steer two independent systems. This result explains the monogamy of two-setting Bell inequality violations and the sensitivity of the continuous variable (CV) EPR criterion to losses on the steering party. We generalize to mmm settings. A second type of monogamy relation gives the quantitative amount of sharing possible, when the number of parties is less than or equal to mmm, and takes a form similar to the Coffman-Kundu-Wootters relation for entanglement. The results enable characterization of the tripartite steering for CV Gaussian systems and qubit Greenberger-Horne-Zeilinger and WWW states.
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.