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The European Physical Journal C

Sharing quantum nonlocality under Hawking effect of a Schwarzschild black hole

Shu-Zheng Yang, Kan He

Published Aug 7, 2025• 6 citations
Publisher

Abstract

Abstract Sharing nonlocality refers to whether the postmeasurement state in a Bell test can be reused to demonstrate nonlocality among multiple observers conducting sequential measurements. It has become one of fascinating and challenging topics in the past decade. In this study, we shift the nonlocality sharing scenario to near the Schwarzschild black hole to explore how Hawking radiation affects sequential nonlocality sharing. In the ideal case without Hawking radiation, Alice and Bob share a maximally entangled pure state. Bob measures his half and then passes it to a second Bob, who repeats the measurement process, and so on. Previous studies have shown that Bob can perform an infinite number of measurements to achieve nonlocality sharing with Alice. If only Alice or Bob is affected by Hawking radiation, the number of shares becomes finite and depends on the Hawking temperature. Unfortunately, when both are exposed to Hawking radiation, sharing nonlocality becomes nearly impossible. However, we can overcome this limitation by introducing auxiliary entangled sources. By adding several observers sharing an entangled state with Alice, we form a star network. Our results indicate that with these auxiliary sources, sequential network nonlocality sharing is achievable within this star network.

DOI
10.1140/epjc/s10052-025-14565-4

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Abstract Sharing nonlocality refers to whether the postmeasurement state in a Bell test can be reused to demonstrate nonlocality among multiple observers conducting sequential measurements. It has become one of fascinating and challenging topics in the past decade. In this study, we shift the nonlocality sharing scenario to near the Schwarzschild black hole to explore how Hawking radiation affects sequential nonlocality sharing. In the ideal case without Hawking radiation, Alice and Bob share a maximally entangled pure state. Bob measures his half and then passes it to a second Bob, who repeats the measurement process, and so on. Previous studies have shown that Bob can perform an infinite number of measurements to achieve nonlocality sharing with Alice. If only Alice or Bob is affected by Hawking radiation, the number of shares becomes finite and depends on the Hawking temperature. Unfortunately, when both are exposed to Hawking radiation, sharing nonlocality becomes nearly impossible. However, we can overcome this limitation by introducing auxiliary entangled sources. By adding several observers sharing an entangled state with Alice, we form a star network. Our results indicate that with these auxiliary sources, sequential network nonlocality sharing is achievable within this star network.
Abstract We transfer the scenario of quantum network nonlocal correlation to the vicinity of a black hole’s event horizon, aiming to evaluate the impact of Hawking effect on network nonlocality within this specific context. In an entanglement swapping network with two bipartite resources and three parties, we examine two scenarios with distinct Hawking radiation locations: one where it affects the endpoint parties’ system and another where it impacts all parties’ system. In both cases, network nonlocality decays due to Hawking radiation and disappears entirely when the Hawking temperature reaches a critical threshold. However, we observe a striking phenomenon: when resource states are maximally entangled and the affected system belongs to the endpoint participants, network nonlocality diminishes but does not vanish throughout the radiation process. Subsequently, we extend our investigation to star and chain networks to evaluate how resource quantity and distribution influence network nonlocality under Hawking radiation. Our results indicate that star networks exhibit greater resilience against Hawking radiation in maintaining nonlocality.
Abstract In this work, we explore the impact of the Hawking effect on quantum nonlocality, specifically the maximum violation of the Bell-CHSH inequality, for both scalar and Dirac fields within Schwarzschild spacetime. We reveal the nuanced behavior of the Bell-CHSH inequality as the Hawking temperature (HT) varies. For scalar fields, we observe distinct degradation patterns in the Bell-CHSH inequality, influenced by the state parameter α and its normalized counterpart 1 − α 2 . In contrast, Dirac fields exhibit two distinct degradation trajectories, each converging to different nonzero minimum values as HT approaches infinity T → ∞ , however, this does not apply to the maximally entangled state. Remarkably, the maximum violation of Bell-CHSH inequality becomes zero for scalar fields at infinite HT, while it stabilizes at a finite nonzero value for Dirac fields. Additionally, the quantum nonlocality robustness of the Dirac fields is stronger than that of the scalar fields. Therefore, this study enhances our understanding of the dynamic characteristics of nonlocality within scalar and Dirac fields near a Schwarzschild black hole.
There exist bipartite entangled states whose violations of Clauser-Horne-Shimony-Holt (CHSH) Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs [Phys. Rev. Lett. 125, 090401 (2020)]. Here we consider its analogues for tripartite systems: a tripartite entangled state is shared among Alice, Bob and multiple Charlies. The first Charlie measures his qubit and then passes his qubit to the next Charlie who measures again with other measurements and so on. The goal is to maximize the number of Charlies that can observe some kind of nonlocality with the single Alice and Bob. It has been shown that at most two Charlies could share genuine nonlocality of the Greenberger-Horne-Zeilinger (GHZ) state via the violation of Svetlichny inequality with Alice and Bob [Quantum Inf. Process. 18, 42 (2019) and Phys. Rev. A 103, 032216 (2021)]. In this work, we show that arbitrarily many Charlies can have standard nonlocality (via violations of Mermin inequality) and some other kind of genuine nonlocality (which is known as genuinely nonsignal nonlocality) with the single Alice and single Bob.
It was showed in [Phys. Rev. Lett. 125 090401 (2020)] that there exist unbounded number of independent Bobs who can share quantum nonlocality with a single Alice by performing sequentially measurements on the Bob’s half of the maximally entangled pure two-qubit state. However, from practical perspectives, errors in entanglement generation and noises in quantum measurements will result in the decay of nonlocality in the scenario. In this paper, we analyze the persistency and termination of sharing nonlocality in the noisy scenario. We first obtain the two sufficient conditions under which there exist n independent Bobs who can share nonlocality with a single Alice under noisy measurements and the noisy initial two qubit entangled state. Analyzing the two conditions, we find that the influences on persistency under different kinds of noises can cancel each other out. Furthermore, we describe the change patterns of the maximal nonlocality-sharing number under the influence of different noises. Finally, we extend our investigation to the case of arbitrary finite-dimensional systems.
Bipartite entangled states whose violations of the Clauser-Horne-Shimony-Holt Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs exist [Brown and Colbeck, Phys. Rev. Lett. 125, 090401 (2020)]. Here we consider their analogs for tripartite systems: a tripartite entangled state is shared among Alice, Bob, and multiple Charlies. The first Charlie measures his qubit and then passes his qubit to the next Charlie, who measures again with other measurements, and so on. The goal is to maximize the number of Charlies that can observe some kind of nonlocality with the single Alice and Bob. It has been shown that at most two Charlies can share genuine nonlocality of the Greenberger-Horne-Zeilinger state via the violation of the Svetlichny inequality with Alice and Bob [S. Saha et al., Quantum Inf. Process. 18, 42 (2019); Zhang and Fei, Phys. Rev. A 103, 032216 (2021)]. In this work, we show that arbitrarily many Charlies can have standard nonlocality (via violations of the Mermin inequality) and some other kind of genuine nonlocality (which is known as genuinely nonsignal nonlocality) with a single Alice and single Bob.
Abstract Bell nonlocality is a valuable resource in quantum information processing tasks. Scientists are interested in whether a single entangled state can generate a long sequence of nonlocal correlations. Previous work has accomplished sequential tripartite nonlocality sharing through unsharp measurements. In this paper, we investigate the sharing of tripartite nonlocality using only projective measurements and sharing classical randomness. For the generalized GHZ state, we have demonstrated that using unbiased measurement choices, two Charlies can share the standard tripartite nonlocality with a single Alice and a single Bob, while at most one Charlie can share the genuine tripartite nonlocality with a single Alice and a single Bob. However, with biased measurement choices, the number of Charlies sharing the genuine tripartite nonlocality can be increased to two. Nonetheless, we find that using biased measurements does not increase the number of sequential observers sharing the standard tripartite nonlocality. Moreover, we provide the feasible range of double violation for the parameters of the measurement combination probability with respect to the state.