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The European Physical Journal C

Enhanced robustness of non-maximal multipartite entanglement under Hawking radiation

Jun-Ming Li, Lei Tong, X. L. Huang

Published Feb 24, 2026• 2 citations
Publisher

Abstract

Abstract It is commonly expected that maximally multipartite entangled states provide the richest quantum correlations and thus represent optimal quantum resources in the Schwarzschild black hole background. Here, by analyzing the genuine N-partite entanglement of fermionic modes near the event horizon, quantified via concurrence, we identify a counterintuitive phenomenon: in this curved spacetime, the genuine multipartite entanglement of a maximally entangled state can be lower than that of a suitably chosen non-maximally entangled state. This observation implies that, from the perspective of quantum resource efficiency, non-maximally entangled multipartite states may outperform their maximal counterparts for quantum information tasks under gravitational effects. Therefore, preparing appropriately engineered non-maximally entangled multipartite states as initial resources provides a more practical and effective approach to quantum information processing in Schwarzschild spacetime.

DOI
10.1140/epjc/s10052-026-15391-y

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Abstract It is commonly expected that maximally multipartite entangled states provide the richest quantum correlations and thus represent optimal quantum resources in the Schwarzschild black hole background. Here, by analyzing the genuine N-partite entanglement of fermionic modes near the event horizon, quantified via concurrence, we identify a counterintuitive phenomenon: in this curved spacetime, the genuine multipartite entanglement of a maximally entangled state can be lower than that of a suitably chosen non-maximally entangled state. This observation implies that, from the perspective of quantum resource efficiency, non-maximally entangled multipartite states may outperform their maximal counterparts for quantum information tasks under gravitational effects. Therefore, preparing appropriately engineered non-maximally entangled multipartite states as initial resources provides a more practical and effective approach to quantum information processing in Schwarzschild spacetime.
Abstract It is commonly assumed that a maximally multipartite entangled state carries greater quantum resources than a non-maximally multipartite entangled state in the relativistic framework. In this work, we analyze genuine N-partite entanglement of fermionic modes near the event horizon of the Garfinkle–Horowitz–Strominger (GHS) black hole, quantified by concurrence. Remarkably, our results reveal that in dilaton spacetime the genuine multipartite entanglement of a maximally entangled state is actually smaller than that of a non-maximally entangled state. From the perspective of quantum resources, this implies that a non-maximally entangled state may outperform a maximally entangled one in the GHS black hole background, in clear contrast to previous expectations. Furthermore, given the experimental challenges in preparing a maximally entangled state and the relative feasibility of preparing a non-maximally entangled state, our findings suggest that employing a suitably chosen non-maximally entangled state as the initial resource in curved spacetime provides a more practical and advantageous strategy for quantum information tasks.
Abstract It is generally believed that quantum entanglement in the maximally entangled states is greater than quantum entanglement in the non-maximally entangled states under a relativistic setting. In this paper, we study quantum entanglement for four different types of Bell-like states of the fermionic modes near the event horizon of a Schwarzschild black hole. It is interesting to find that quantum entanglement in the maximally entangled states is less than quantum entanglement in the non-maximally entangled states in Schwarzschild spacetime. From the perspective of quantum resources, the non-maximally entangled states may have more advantages in curved spacetime compared to the maximally entangled states. This is obviously different from the conclusions in previous paper. For two types of Bell-like states, quantum entanglement suffers sudden death under the Hawking effect of the black hole, and for the other two types of Bell-like states, quantum entanglement can exist forever regardless of the Hawking temperature. Therefore, we should choose appropriate types of Bell-like states to handle relativistic quantum information tasks.
We investigate quantum entanglement and coherence for four classes of Bell-like fermionic states in the vicinity of the event horizon of a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. Contrary to the common expectation that maximally entangled states always provide superior quantum resources, our results show that their entanglement can be lower than that of suitably chosen non-maximally entangled states in this curved spacetime background. This reveals that non-maximally entangled states may offer operational advantages for entanglement-based tasks under gravitational effects. In contrast, quantum coherence exhibits monotonic behavior: larger initial coherence leads to systematically enhanced robustness against the dilaton induced degradation. These results indicate that the optimal choice of initial quantum states depends sensitively on the specific quantum resource, either quantum entanglement or quantum coherence, required for quantum information processing near a dilaton black hole.
We investigate quantum entanglement and coherence for four classes of Bell-like fermionic states in the vicinity of the event horizon of a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. Contrary to the common expectation that maximally entangled states always provide superior quantum resources, our results show that their entanglement can be lower than that of suitably chosen non-maximally entangled states in this curved spacetime background. This reveals that non-maximally entangled states may offer operational advantages for entanglement-based tasks under gravitational effects. In contrast, quantum coherence exhibits monotonic behavior: larger initial coherence leads to systematically enhanced robustness against the dilaton induced degradation. These results indicate that the optimal choice of initial quantum states depends sensitively on the specific quantum resource, either quantum entanglement or quantum coherence, required for quantum information processing near a dilaton black hole.
Abstract Complex quantum information tasks in a gravitational background require multipartite entanglement for effective processing. Therefore, it is necessary to investigate the properties of multipartite entanglement in a relativistic setting. In this paper, we study genuine N-partite entanglement of massless Dirac fields in the Schwarzschild-de Sitter (SdS) spacetime, characterized by the presence of a black hole event horizon (BEH) and a cosmological event horizon (CEH). We obtain the general analytical expression of genuine N-partite entanglement shared by n observers near BEH and m ( n+m=Nn+m=Nn+m=N n + m = N ) observers near CEH. It is shown that genuine N-partite entanglement monotonically decreases with the decrease of the mass of the black hole, suggesting that the Hawking effect of the black hole destroys quantum entanglement. It is interesting to note that genuine N-partite entanglement is a non-monotonic function of the cosmological constant, meaning that the Hawking effect of the expanding universe can enhance quantum entanglement. This result contrasts with multipartite entanglement in single-event horizon spacetime, offering a new perspective on the Hawking effect in multi-event horizon spacetime.
Gravitational effects associated with black holes are widely believed to universally degrade quantum entanglement, with the loss of maximal entanglement being particularly severe and even irreversible for bosonic fields. In this work, we investigate the entanglement properties of the four-qubit cluster state (CL4CL_4CL4​) for fermionic fields in the curved spacetime of a Schwarzschild black hole. Remarkably, we uncover a counterintuitive phenomenon: as the Hawking temperature increases, quantum entanglement (111-333 tangle) of the CL4CL_4CL4​ state remains strictly constant, indicating a ``complete freezing of initially maximal entanglement". This constitutes the first explicit example in which maximal entanglement remains perfectly preserved in a black hole environment, defying the conventional expectation that gravitational effects can only suppress maximal quantum correlations. Moreover, our results indicate that, within a relativistic framework, the CL4CL_4CL4​ state constitutes a high-quality quantum resource with potential applications in relativistic quantum information processing, and may significantly improve the performance of such protocols.