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.

Quantum network correlations are crucial for long-distance quantum communication, quantum cryptography, and distributed quantum computing. Detecting network steering is particularly challenging in complex network structures. We have studied the steering inequality criteria for a 2-forked 3-layer tree-shaped network. Assuming the first and third layers are trusted and the second layer is untrusted, we derived a steering inequality criterion using the correlation matrix between trusted and untrusted observables. In particular, we apply the steering criterion to three classes of measurements which are of special significance: local orthogonal observables, mutually unbiased measurements, and general symmetric informationally complete measurements. We further illustrate the effectiveness of our method through an example.

Previous studies have shown that quantum nonlocality can theoretically be shared infinitely, but this relies on the precise implementation of measurement schemes. However, in practice, experimenters often struggle to precisely control measurement devices to perfectly align with the target measurements, inevitably introducing measurement error. To address this issue, we introduce an operational notion of inaccuracy that can be directly estimated in the laboratory to formalize the problem. Based on this method, we investigate the impact of imprecise measurements on infinite nonlocality sharing. We first consider the scenario where participants use imprecise measurements to detect nonlocal correlations via the Clauser-Horne-Shimony-Holt (CHSH) inequality and prove the necessary and sufficient conditions for determining the maximum number of shares based on measurement error. Building on this condition, we conduct detailed numerical analyses, the results of which indicate that even minor alignment error can significantly limit the number of nonlocality shares. Finally, we extend our research to the tripartite sequential sharing scenario.