Recently, much attention have been paid to the constructions of nonlocal multipartite orthogonal product states. Among the existing results, some are relatively complex in structure while others have many constraint conditions. In this paper, we first give a simple method to construct a nonlocal set of orthogonal product states in ${\otimes }_{j=1}^n{\mathbb{C}}^d$, where $d,n$ are two positive integers, $d\ge 2$ and $n\ge 3$. Then we give a proof for local indistinguishability of the set constructed by our method. According to the characteristics of this construction method, we get a new construction of nonlocal set with fewer states in the same quantum system. Furthermore, we generalize these two results to a more general ${\otimes }_{j=1}^n{\mathbb{C}}^{d_j}$ quantum system, where $n,d_j$ are two positive integers, $n\ge 3$ and $d_j\ge 2$. Compared with the existing results, the nonlocal set of multipartite orthogonal product states constructed by our method has fewer elements and is simpler. Most of all, our multipartite constructions are more general than the ones reported earlier.

• Received 17 March 2020
• Accepted 12 August 2020

DOI:https://doi.org/10.1103/PhysRevA.102.032211