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 2 n 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 <?CDATA (C³)⊗ 6?> ( C 3 ) ⊗ 6 and <?CDATA (C⁴)⊗ 6?> ( C 4 ) ⊗ 6 are given. Finally, we construct nonlocal orthogonal product states in <?CDATA (Cᵈ)⊗ 2n?> ( C d ) ⊗ 2 n and discuss the cases where d is odd and even. Our results demonstrate the phenomenon of nonlocality without entanglement in a 2 n -partite system.