In this paper, we mainly study the local indistinguishability of mutually orthogonal product basis quantum states in the high-dimensional quantum systems. In the Hilbert space of 3 circle times 3, Walgate and Hardy [Phys. Rev. Lett. 89, 147901 ( 2002)] presented a very simple proof for nonlocality of nine orthogonal product basis quantum states which are given by Bennett et al. [Phys. Rev. A 59, 1070 ( 1999)]. In the quantum system of d circle times d, where d is odd, we construct d(2) orthogona
