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arXiv:2208.08587 · The European Physical Journal C

Fermionic steering and its monogamy relations in Schwarzschild spacetime

Shu-Min Wu, Hao‐Sheng Zeng

Published Aug 17, 2022• 36 citations
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Abstract

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.

DOI
10.1140/epjc/s10052-022-10679-1

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Laser Physics Letters•Mar 14, 2018•4 citations
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 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.
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 investigate quantum steering of Dirac field for different types of Bell states in Schwarzschild–de Sitter (SdS) spacetime that has a black hole event horizon (BEH) and a cosmological event horizon (CEH). We find that fermionic steerability from Bob to Alice is greater than fermionic steerability from Alice to Bob, while bosonic steerability exhibits the opposite behavior in SdS spacetime. These different properties between fermionic and bosonic steering arise from the differences between Fermi–Dirac statistics and Bose–Einstein statistics. We also find that the Hawking effect of the black hole decreases fermionic steerability. However, the Hawking effect of the expanding universe can enhance fermionic steerability, which differs from the properties of quantum steering in single-event horizon spacetime. Interestingly, we can indirectly protect quantum steering by using appropriate types of Bell states in multi-event horizon spacetime. These conclusions are helpful to guide the task of processing relativistic quantum information for quantum steering in SdS 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 study the redistribution of the fermionic steering and the relation among fermionic Bell nonlocality, steering, and entanglement in the background of the Garfinkle–Horowitz–Strominger dilaton black hole. We analyze the meaning of the fermionic steering in terms of the Bell inequality in curved spacetime. We find that the fermionic steering, which is previously found to survive in the extreme dilaton black hole, cannot be considered to be nonlocal. We also find that the dilaton gravity can redistribute the fermionic steering, but cannot redistribute Bell nonlocality, which means that the physically inaccessible steering is also not nonlocal. Unlike the inaccessible entanglement, the inaccessible steering may increase non-monotonically with the dilaton. Furthermore, we obtain some monogamy relations between the fermionic steering and entanglement in dilaton spacetime. In addition, we show the difference between the fermionic and bosonic steering in curved spacetime.
Abstract In this paper, we deduce the vacuum structure for Dirac fields in the background of Schwarzschild space-time beyond the single-mode approximation and discuss the performance of quantum entanglement between particle and antiparticle modes of a Dirac field with Hawking effect. It is shown that Hawking radiation does not always destroy the physically accessible entanglement, and entanglement amplification may happen in some cases. This striking result is different from that of the single-mode approximation, which holds that the Hawking radiation can only destroy entanglement. Lastly, we analyze the physically accessible entanglement relation outside the event horizon and demonstrate that the monogamy inequality is constantly established regardless of the choice of given parameters.