The local indistinguishability of multipartite product states

In this paper, we mainly study the local indistinguishability of multipartite product states. Firstly, we follow the method of Z.-C. Zhang \emph{et al}[Phys. Rev. A 93, 012314(2016)] to give another more concise set of $2n-1$ orthogonal product states in $\mathbb{C}^m\otimes\mathbb{C}^n(4\leq m\leq n)$ which can not be distinguished by local operations and classical communication(LOCC). Then we use the 3 dimension cubes to present some product states which give us an intuitive view how to construct locally indistinguishable product states in tripartite quantum system. At last, we give an explicit construction of locally indistinguishable orthogonal product states for general multipartite system.