Quantum entanglement as a resource to locally distinguish orthogonal product states

Recently, Zhang et al. constructed one family of orthogonal product states which cannot be perfectly distinguished by local operations and classical communication (LOCC) in the 2m⊗2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2m\otimes 2n$$\end{document} quantum system with m,n≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m,n\ge 2$$\end{document} (Sci Rep 6: 28864, 2016). However, it is an interesting question that what entanglement resources are necessary and/or sufficient for this task to be possible with LOCC. In this paper, we study the local distinguishability of mutually orthogonal product states with quantum entanglement as an auxiliary resource. Specifically, we put forward that the locally indistinguishable orthogonal product states in a low-dimensional system can be locally distinguished with certainty merely by utilizing an additional 2⊗2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\otimes 2$$\end{document} maximally entangled state. Then, we generalize the distinguishing method to the states in 2m⊗2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2m\otimes 2n$$\end{document}. These results reveal the phenomenon of less nonlocality with more entanglement. And they enable us to better understand the role of quantum entanglement in the local discrimination of quantum states and the relationship between entanglement and nonlocality.