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arXiv:2209.11402

Genuine Bell locality and nonlocality in the networks

Li‐Yi Hsu

Published Sep 23, 2022• 0 citations
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Abstract

In the literature on $K$-locality ($K\geq2$) networks, the local hidden variables are strictly distributed in the specific observers rather than the whole ones. Regarding genuine Bell locality, all local hidden variables, as classical objects that allow for perfect cloning in classical physics, should be cloned and then spread throughout the networks. More correlators are involved in the proposed linear and non-linear Bell-type inequalities, where their upper bounds are specified by the pre-determined output probability distribution. As for the quantum version, the no-clone theorem limits the broadcast of quantum correlations. To explore genuine Bell nonlocality in variant particle distributions in the networks, the Pauli operators stabilizing the two-qubit Bell states or multi-qubit Greenberger--Horne--Zeilinger states (GHZ states) play an essential role in designing the proposed linear and non-linear Bell tests and assigning the local incompatible measurements for the spatially separated observers. We prove the maximal violations of the proposed Bell-type inequalities quantum networks. In the end, how entanglement swapping replaces the joint measurements in the Bell tests is demonstrated.

DOI
10.48550/arxiv.2209.11402

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In the literature on KKK-locality (K≥2K\geq2K≥2) networks, the local hidden variables are strictly distributed in the specific observers rather than the whole ones. Regarding genuine Bell locality, all local hidden variables, as classical objects that allow for perfect cloning in classical physics, should be cloned and then spread throughout the networks. More correlators are involved in the proposed linear and non-linear Bell-type inequalities, where their upper bounds are specified by the pre-determined output probability distribution. As for the quantum version, the no-clone theorem limits the broadcast of quantum correlations. To explore genuine Bell nonlocality in variant particle distributions in the networks, the Pauli operators stabilizing the two-qubit Bell states or multi-qubit Greenberger--Horne--Zeilinger states (GHZ states) play an essential role in designing the proposed linear and non-linear Bell tests and assigning the local incompatible measurements for the spatially separated observers. We prove the maximal violations of the proposed Bell-type inequalities quantum networks. In the end, how entanglement swapping replaces the joint measurements in the Bell tests is demonstrated.
Abstract In K-locality networks, local hidden variables emitted from classical sources are distributed among limited observers. We explore genuine Bell locality in classical networks, where, regarding all local hidden variables as classical objects that can be perfectly cloned and spread throughout the networks, any observer can access all local hidden variables plus shared randomness. In the proposed linear and nonlinear Bell-type inequalities, there are more correlators to reveal genuine Bell locality than those in the K-locality inequalities, and their upper bounds can be specified using the probability normalization of the predetermined probability distribution. On the other hand, the no-cloning theorem limits the broadcast of quantum correlations in quantum networks. To explore genuine Bell nonlocality, the stabilizing operators play an important role in designing the segmented Bell operators and assigning the incompatible measurements for the spatially separated observers. We prove the maximal violations of the proposed Bell-type inequalities tailored for the given qubit distributions in quantum networks.
Genuine multipartite nonlocality and nonlocality arising in networks composed of several independent sources have been separately investigated. While some genuinely entangled states cannot be verified by violating a single Bell-type inequality, a quantum network consisting of different sources allows for the certification of the non-classicality of all sources. In this paper, we propose the first method to verify both types of nonlocality simultaneously in a single experiment. We consider a quantum network comprising a bipartite source and a tripartite source. We demonstrate that there are quantum correlations cannot be simulated if the tripartite source distributes biseparable systems while the bipartite source distributes even stronger-than-quantum systems. These correlations can be used to verify both the genuine multipartite nonlocality of generalized Greenberger-Horne-Zeilinger states and the full network nonlocality that is stronger than all the existing results. Experimentally, we observe both types of nonlocality in a high fidelity photonic quantum network by violating a single network Bell inequality.
Bell nonlocality is the experimentally testable incompatibility between quantum correlations and explanations based on local hidden variables. Its significance now extends beyond the foundations of quantum mechanics: a Bell-inequality violation can certify entanglement, randomness, measurement incompatibility, and cryptographic security without requiring a detailed model of the devices producing the observed data. This article develops the mathematical structure of Bell experiments and explains its role in device-independent quantum information. Conditional probability distributions are classified into local, quantum, and no-signalling sets; the Clauser-Horne-Shimony-Holt inequality is derived, and its classical, quantum, and algebraic limits are distinguished. Tsirelson’s bound is obtained from the CHSH operator, while Popescu-Rohrlich correlations demonstrate that no-signalling alone does not identify the quantum set. The relation between entanglement and nonlocality is examined through local entangled states, hidden nonlocality, and activation. Nonlocal games, semidefinite relaxations, self-testing, certified randomness, and device-independent quantum key distribution are treated as operational consequences of Bell violation. Particular attention is given to entropy accumulation, finite-data security, loophole-free experiments, and the limitations of device independence. Bell nonlocality emerges as both a foundational separation between classical and quantum causal models and a quantitative resource for cryptographic and informational tasks.
Genuine multipartite nonlocality and nonlocality arising in networks composed of several independent sources have been investigated separately. While some genuinely entangled states cannot be verified by violating a single Bell-type inequality, a quantum network consisting of different sources enables the certification of the nonclassicality of all sources. In this Letter, we propose the first method to verify both types of nonlocality simultaneously in a single experiment. We consider a quantum network comprising a bipartite source and a tripartite source. We demonstrate that there are quantum correlations that cannot be simulated if the tripartite source distributes biseparable systems while the bipartite source distributes even stronger-than-quantum systems. These correlations can be used to verify both the genuine multipartite nonlocality of generalized Greenberger-Horne-Zeilinger states and the full network nonlocality that is stronger than all the existing results. Experimentally, we observe both types of nonlocality in a high-fidelity photonic quantum network by violating a single network Bell inequality.
In practical quantum networks, a variety of multi-qubit stabilized states emitted from independent sources are distributed among the agents, and the correlations across the entire network can be derived from each agent's local measurements on the shared composite quantum systems. To reveal the Bell non-locality in such cases as a quantum feature, minimal knowledge of the emitted stabilizer state is required. Here, we demonstrate that knowing the stabilizing and logical operators indeed provides a new way of exploring Bell non-locality in quantum networks. For the qubit distribution in quantum networks, the associated nonlinear Bell inequalities are derived. On the other hand, to violate these inequalities, one can design local incompatible observables using minimal knowledge of the emitted states. The tilted nonlinear Bell inequalities tailored for specific non-maximal entangled stabilizer states and a way of achieving the maximal violation are also explored.
While Bell nonlocality of a bipartite system is counterintuitive, multipartite nonlocality in our many-body world turns out to be even more so. Recent theoretical study reveals in a theory-agnostic manner that genuine multipartite nonlocal correlations cannot be explained by any causal theory involving fewer-partite nonclassical resources and global shared randomness. Here, we provide a Bell-type inequality as a test for genuine multipartite nonlocality in network by exploiting a matrix representation of the causal structure of a multipartite system. We further present experimental demonstrations that both four-photon GHZ state and generalized four-photon GHZ state significantly violate the inequality, i.e., the observed four-partite correlations resist explanations involving three-way nonlocal resources subject to local operations and common shared randomness, hence confirming that nature is boundless multipartite nonlocal.