Local distinguishability of orthogonal quantum states helps reduce quantum resource consumption in quantum protocols. This report introduces our two works on the LOCC distinguishability of orthogonal product states (OPSs). The first work investigates four multipartite OPSs in high-dimensional systems. We propose the vector counting pairwise orthogonal relations to classify four tripartite OPSs (any pair orthogonal on only one subsystem) into three categories. We prove that OPSs from two categories are perfectly LOCC distinguishable. Notably, two sets with identical orthogonal graphs may have different distinguishability, meaning the orthogonal graph alone is insufficient to judge LOCC distinguishability. We also derive the distinguishability conditions for the remaining category, and give sufficient conditions based on the number of orthogonal pairs for tripartite and multi-partite systems. The second work focuses on five OPSs over bipartite and tripartite systems. For bipartite five OPSs with pairwise orthogonality restricted to a single subsystem, all but one case are LOCC distinguishable. For tripartite five OPSs, all cases except two are perfectly distinguishable, and we analyze these two exceptional cases. Our results offer a systematic characterization of the LOCC discrimination of four and five OPSs, enriching the study of local distinguishability for orthogonal product states.

徐光宝，男，1980年11月出生，博士（硕士）生导师，北京邮电大学计算机科学与技术专业博士毕业。中国计算机学会、中国密码学会、中国电子学会会员；中国计算机学会量子计算专委会执行委员。主要研究方向和研究兴趣：信息安全与密码学、量子信息处理与量子密码、量子图像处理。主持国家自然科学基金(面上项目)1项、山东省自然科学基金(面上项目)2项、北京邮电大学网络与交换技术国家重点实验室开放课题1项。参与国家自然科学基金面上项目和青年基金项目各1项、山东省自然科学基金面上项目2项、山东省科技计划项目2项、山东省重点研发项目1项。发表SCI检索论文80余篇，其中中科院分区为2区及以上的论文20余篇，高被引论文2篇。目前担任国际知名期刊《Quantum Information Processing》副主编和《山东科技大学学报》的青年编委，是《Physical Review A》、《International Journal of Theoretical Physics》、《Modern Physics Letters B》等国际期刊的审稿人。