Locally distinguishing multipartite orthogonal product states with different entanglement resource

Abstract

Recently, entanglement-assisted state discrimination has attracted much attention. However, most of the relevant results are about the bipartite quantum states and very little is known about the multipartite case. In this paper, considering the nonlocal orthogonal product states constructed by Jiang and Xu [Phys. Rev. A 102, 032211 (2020)], we first present one protocol to locally distinguish a set of orthogonal product states in $$3\otimes 3 \otimes 3$$ by using a $$2\otimes 2$$ maximally entangled state. Then, we generalize the distinguishing method for the class of nonlocal of orthogonal product states in $$\otimes _{j=1}^n{\mathbb {C}}^{d_j}$$ , where $$n\geqslant 3, d_j\geqslant 2, j=1,2,\ldots ,n$$ . Furthermore, for another class of orthogonal product states in $$\otimes _{j=1}^n{\mathbb {C}}^{d_j}$$ , where $$n\geqslant 3, d_j\geqslant 3, j=1,2,\ldots ,n$$ , we prove that these states can also be distinguished by LOCC with a $$3\otimes 3$$ maximally entangled state or two copies of $$2\otimes 2$$ maximally entangled states. The above results can let us better understand how to use entanglement resource more efficiently in multipartite quantum systems and also reveal the phenomenon of less nonlocality with more entanglement.