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Quantum nonlocality, as an invaluable quantum resource, plays an indispensable key role in numerous quantum information processing tasks. Accurate characterization and effective detection of nonlocality have always been important and challenging topics in theoretical research and experimental exploration of quantum information. How to precisely identify and verify the phenomenon of quantum nonlocality in complex many-body quantum systems, and how to design more efficient detection methods for nonlocality, have become important scientific issues that need to be solved urgently. This paper is dedicated to the detection of multipartite quantum nonlocality, with a focus on exploring how to achieve the detection of multipartite quantum nonlocality using the Svetlichny inequality. Firstly, the maximum quantum violation of the Svetlichny inequality is discussed. Through construction, a quantum state $\rho_0$ and a set of observables $\mathcal{A}_0$ are obtained, which achieve the maximum quantum violation of the Svetlichny inequality. It is also demonstrated how to construct other quantum states and sets of observables to achieve its maximum violation, thereby clarifying that the quantum states and sets of observables that achieve the maximum quantum violation of the Svetlichny inequality are not unique. Secondly, in order to find more quantum states and sets of observables that violate the Svetlichny inequality, the corresponding Hamiltonian was constructed using the Svetlichny operator. This core issue of finding quantum states that violate the Svetlichny inequality was ingeniously transformed into solving the ground state of this Hamiltonian. Leveraging the powerful function approximation capability of neural networks, neural network quantum states were constructed. Two optimization algorithms, the Nelder-Mead simplex method and Quantum Variational Monte Carlo (VMC), were respectively adopted to optimize the network parameters in order to find the ground state energy and ground state of the Hamiltonian, thereby achieving the violation of the Svetlichny inequality and ultimately detecting nonlocal states. To ensure the efficiency and accuracy of the detection method, this paper conducts a comparative study of different optimization methods. By comparing the Nelder-Mead simplex method with the VMC method, it is found that the VMC method is more suitable for nonlocality detection based on neural network quantum states in terms of efficiency and accuracy, providing reliable computational support for the detection of many-body quantum nonlocality and the violation of the Svetlichny inequality. To verify the validity and universality of the proposed method, the nonlocality of multipartite quantum pure states were detected using neural network quantum states and the VMC method under different Hamiltonians. The results demonstrate that this method successfully captures violations of the Svetlichny inequality in many-body quantum systems, thereby achieving effective detection of multipartite quantum nonlocality. This fully confirms the validity and universal potential of the VMC method in nonlocality detection based on neural network quantum states. This study not only verifies the theoretical and technical feasibility of the detection of multipartite quantum nonlocality based on neural network quantum states and the VMC method, but also provides valuable new insights for the field of nonlocality detection. More importantly, it opens up a new research avenue for solving complex quantum many-body problems using neural networks.
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Keywords:
- nonlocality /
- neural network quantum state /
- Svetlichny inequality /
- VMC /
- detection
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