In recent years, using entanglement resources to assist the local discrimination of orthogonal quantum states has attracted wide attention. However, many studies mainly focus on entanglement-assisted local discrimination in bipartite systems, and there are relatively few in multipartite states. In this paper, for the nonlocal set of \(3d-3\) orthogonal product states in \(d\otimes d\otimes d\) \((d\ge 3)\) constructed by Zhu et al. (Quantum Inf. Process. 21, 252, 2022), we propose a method of using an ancillary \(d\otimes d\) maximally entangled state to realize the local perfect discrimination. Firstly, with a \(3\otimes 3\) maximally entangled state as an auxiliary resource, we present a method to exactly identify the locally indistinguishable 6 orthogonal product states in \(3\otimes 3\otimes 3\) by local operations and classical communication (LOCC). Then the distinguishing method can be generalized to the \(3d-3\) states in \(d\otimes d\otimes d\) . These results not only reveal the phenomenon of less nonlocality with more entanglement, but also help us better realize the usefulness of entanglement in the local discrimination of quantum states.
