Quantum nonlocality without entanglement in a 2n-partite system

In recent years, researchers focused their attention on the construction of nonlocal product states in multipartite quantum systems. This paper proposes a novel partitioning method for multipartite quantum systems, aiming to improve the operation efficiency. Firstly, we divide 2n subsystems into n parts two by two and implement orthogonality-preserving local measurement on the partitioned composite systems. Subsequently, based on the partitioning mode, nonlocal orthogonal product states in (C-3)(circle times 6) and (C-4)(circle times 6) are given. Finally, we construct nonlocal orthogonal product states in (C-d)(circle times 2n) and discuss the cases where d is odd and even. Our results demonstrate the phenomenon of nonlocality without entanglement in a 2n-partite system.