Recently, Yuan et al. (Phys Rev A 102:042228, 2020) construct a set of strongly nonlocal orthogonal product states in \(\mathbb {C}^{d} \otimes \mathbb {C}^{d} \otimes \mathbb {C}^{d}\) , where \(d \ge 3\) . Then, it is interesting how much entanglement resource is sufficient to locally distinguish these states, and very little is known about entanglement-assisted distinguishing strongly nonlocal quantum states. In this paper, we first design one entanglement-assisted state discrimination protocols for strongly nonlocal orthogonal product states in \(\mathbb {C}^{4} \otimes \mathbb {C}^{4} \otimes \mathbb {C}^{4}\) quantum system. Then, in the same way, we give how much entanglement resource is sufficient to locally distinguish these strongly nonlocal orthogonal product states in \(\mathbb {C}^{5} \otimes \mathbb {C}^{5} \otimes \mathbb {C}^{5}\) , \(\mathbb {C}^{6} \otimes \mathbb {C}^{6} \otimes \mathbb {C}^{6}\) quantum systems. Finally, we propose a conjecture that less entanglement resource than quantum teleportation can be used to locally distinguish these strongly nonlocal quantum states in \(\mathbb {C}^{d} \otimes \mathbb {C}^{d} \otimes \mathbb {C}^{d}\) , where \(d \ge 3\) . The above results can illustrate the important role of entanglement resource in locally distinguishing orthogonal quantum states and also reveal the phenomenon of less nonlocality with more entanglement.
