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The European Physical Journal C

Quantum steering of GHZ and W states in relativistic motion

Si-Han Shang, Shu-Min Wu

Published Jul 21, 2025• 6 citations
Publisher

Abstract

Abstract We investigate tripartite quantum steering dynamics in a three-Unruh–DeWitt-detector system, examining both $$1\rightarrow 2$$ 1 → 2 (i.e., from Alice to Bob and Charlie) and $$2\rightarrow 1$$ 2 → 1 steering (i.e., from Alice and Bob to Charlie) configurations under two paradigmatic entangled initial states: the Greenberger–Horne–Zeilinger (GHZ) and W states. Our analysis demonstrates that $$1\rightarrow 2$$ 1 → 2 steering exhibits better resistance to Unruh decoherence than $$2\rightarrow 1$$ 2 → 1 steering. Notably, the $$1\rightarrow 2$$ 1 → 2 steering of the W state displays a non-monotonic dependence on the acceleration parameter, indicating that the Unruh effect can, in certain regimes, enhance quantum steering. These results suggest that the Unruh effect plays a dual role in tripartite quantum systems, as it can both enhance and degrade quantum steering. Consequently, moving beyond the conventional interpretation of the Unruh effect as merely a source of decoherence, our study provides a new insight by exploring tripartite quantum steering in a relativistic setting.

DOI
10.1140/epjc/s10052-025-14516-z

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Abstract We investigate tripartite quantum steering dynamics in a three-Unruh–DeWitt-detector system, examining both 1→21\rightarrow 21→2 1 → 2 (i.e., from Alice to Bob and Charlie) and 2→12\rightarrow 12→1 2 → 1 steering (i.e., from Alice and Bob to Charlie) configurations under two paradigmatic entangled initial states: the Greenberger–Horne–Zeilinger (GHZ) and W states. Our analysis demonstrates that 1→21\rightarrow 21→2 1 → 2 steering exhibits better resistance to Unruh decoherence than 2→12\rightarrow 12→1 2 → 1 steering. Notably, the 1→21\rightarrow 21→2 1 → 2 steering of the W state displays a non-monotonic dependence on the acceleration parameter, indicating that the Unruh effect can, in certain regimes, enhance quantum steering. These results suggest that the Unruh effect plays a dual role in tripartite quantum systems, as it can both enhance and degrade quantum steering. Consequently, moving beyond the conventional interpretation of the Unruh effect as merely a source of decoherence, our study provides a new insight by exploring tripartite quantum steering in a relativistic setting.
Abstract We investigate the behavior of (1 → 2) and (2 → 1) genuine tripartite EPR steering in generalized GHZ (GGHZ) states when observers undergo relativistic acceleration, and extend the analysis to network quantum steering in linear networks composed of two Bell states. Within the free Dirac field framework, our results demonstrate that both types of genuine tripartite steering and network steering exhibit monotonic degradation with increasing acceleration. In the single-accelerator scenario, all steering types persist even at infinite acceleration, while physically inaccessible (2 → 1) genuine steering emerges at high accelerations. Strikingly contrasting behavior is observed when two observers accelerate, where sudden death of steering occurs in all cases. Furthermore, we study the dynamical evolution of both genuine tripartite steering and network quantum steering in noninertial frames when one accelerated qubit undergoes decoherence. We reveal a hierarchy of sensitivity for both steering types to different decoherence noises in noninertial frames, and find that genuine tripartite steering and network quantum steering are more sensitive to quantum decoherence effects than to the Unruh effect.
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 In this letter, the dynamic behavior of Einstein–Podolsky–Rosen (EPR) steering and the redistribution of EPR steering under a relativistic framework are investigated. Specifically, we explore the scenario that particle A held by Alice is in a flat space–time and another particle B held by Bob entangled with A is in a non-inertial framework. The results show that EPR steering from Alice to Bob is dramatically destroyed by the Unruh effect caused by the acceleration of Bob. Besides, EPR steering possess asymmetry, and EPR steering asymmetry increases with growing intensity of the Unruh effect, implying that the Unruh effect can bring about EPR steering asymmetry. Furthermore, the reduced physically accessible EPR steering from Alice to Bob is distributed to the physically inaccessible EPR steering (from Alice to anti-Bob or from Bob to anti-Bob). Notably, unlike entanglement and quantum discord, only one of the EPR steering from Alice to anti-Bob and Bob to anti-Bob experiences a sudden birth with increase in the acceleration parameter, which means that they cannot simultaneously survive. That is, the monogamous relationship of EPR steering is still tenable in such a scenario. Consequently, we believe that EPR steering could also serve as an important information resource within long-distance quantum secure communication under the relativistic framework.
We investigate directional quantum steering harvesting by two uniformly accelerated non-identical Unruh-DeWitt detectors coupled to a massless scalar field in the Minkowski vacuum. We show that the Unruh effect does not simply degrade harvested steering, but can reshape its directionality in a strongly parameter-dependent manner. At low detector energy scales, acceleration predominantly suppresses steering, whereas at higher energy scales, moderate acceleration can enhance steering and even activate an initially absent steering direction. Most strikingly, within a finite acceleration window, the Unruh effect enhances steering in one direction while simultaneously suppressing it in the opposite direction, revealing an intrinsically directional influence of relativistic acceleration. Detector non-identicality provides an additional control mechanism: a moderate energy-gap mismatch can enhance or activate one steering direction while suppressing the reverse one, whereas sufficiently large energy-gap mismatch suppresses the harvested steering. Moreover, the maximal steering asymmetry approximately marks the transition from two-way to one-way steering. Our results establish relativistic acceleration and detector non-identicality as means of controlling the strength and directionality of vacuum-harvested quantum correlations.
Abstract Quantum coherence, a fundamental aspect of quantum mechanics, plays a crucial role in various quantum information tasks. However, preserving coherence under extreme conditions, such as relativistic acceleration, poses significant challenges. In this paper, we investigate the influence of Unruh temperature and energy levels on the evolution of maximal steered coherence (MSC) for different initial states. Our results reveal that MSC is strongly dependent on Unruh temperature, exhibiting behaviors ranging from monotonic decline to non-monotonic recovery, depending on the initial state parameter Δ0\Delta _0Δ0​ Δ 0 . Notably, when Δ0=1\Delta _0=1Δ0​=1 Δ 0 = 1 , MSC is generated as Unruh temperature increases. Additionally, we observe that higher energy levels help preserve or enhance MSC in the presence of Unruh effects. These findings offer valuable insights into the intricate relationship between relativistic effects and quantum coherence, with potential applications in developing robust quantum technologies for non-inertial environments.
A bstract Previous studies have shown that the Unruh effect completely destroys quantum entanglement and coherence of bipartite states, as modeled by entangled Unruh-DeWitt detectors. But does the Unruh effect have a different impact on quantum entanglement of multipartite states within this framework? In this paper, we investigate the influence of the Unruh effect on 1 − 3 entanglement in the context of entangled tetrapartite Unruh-DeWitt detectors. We find that quantum entanglement of tetrapartite W state first decreases to a minimum value and then increases to a fixed value with the growth of the acceleration. This indicates that the Unruh effect can, under certain conditions, enhance quantum entanglement. In other words, the Unruh effect plays a dual role in the behavior of quantum entanglement-both diminishing and enhancing it. This discovery challenges and overturns the traditional view that the Unruh effect is solely detrimental to quantum entanglement and coherence in entangled Unruh-DeWitt detectors, offering a fresh and profound perspective on its impact.