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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3d-3$$\end{document} orthogonal product states in d circle times d circle times d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\otimes d\otimes d$$\end{document}(d >= 3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(d\ge 3)$$\end{document} constructed by Zhu et al. (Quantum Inf. Process. 21, 252, 2022), we propose a method of using an ancillary d circle times d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\otimes d$$\end{document} maximally entangled state to realize the local perfect discrimination. Firstly, with a 3 circle times 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\otimes 3$$\end{document} maximally entangled state as an auxiliary resource, we present a method to exactly identify the locally indistinguishable 6 orthogonal product states in 3 circle times 3 circle times 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\otimes 3\otimes 3$$\end{document} by local operations and classical communication (LOCC). Then the distinguishing method can be generalized to the 3d-3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3d-3$$\end{document} states in d circle times d circle times d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\otimes d\otimes d$$\end{document}. 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.
