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讲座:A Note on Pretty Good State Transfer on Cayley Graphs over Dihedral Groups

    主讲人:曹喜望

    主讲人工作单位:南京航空航天大学

    时间:2019年6月5日 16:00

    地点:光琼科学楼东报告厅 

    主讲人简介:曹喜望,南京航空航天大学理学院教授,博士生导师。师从樊恽教授获得硕士学位,师从北京大学丘维声教授获得博士学位。研究方向是有限域及其应用,在差集、指数和、有限域上的多项式、量子信息处理以及代数编码方面做出了出色的工作,其研究成果发表在相关领域的权威期刊IEEE Transaction on Information TheoryFinite Fields and their ApplicationsDesign Codes and CryptographyScience ChinaMathematics)等,发表学术论文90余篇,出版专著一部。曹喜望教授先后多次访问过Sydney大学、香港科技大学、台湾中央研究院、北京国际数学中心、南开大学陈省身数学研究所等。2010年入选江苏省“青蓝工程”学术带头人,现为国家自然科学基金项目函审人、美国数学会会员、美国数学评论评论员、International Mathematical Union会员、10多家国际SCI/EI期刊审稿人。主持国家自然科学基金面上项目和省部级科研项目多项。2017年获得江苏省科学技术奖。 

     讲座主要内容: The transition matrix of a graph Γ with the adjacency matrix A is defined by H(t) := exp(??tA), where t  R and ? = √?1. The graph is said to admit a pretty good state transfer between a pair of vertices u and v if for any ε > 0, there is a time t such that |e^tvH(t)eu| ≥ 1?ε. The state transfer is perfect if the above inequality holds for ε = 0. Perfect (pretty good) state transfer on graphs has received extensive attention recently due to their significant applications in quantum information processing and quantum computations. However, most of the graphs previously investigated are abelian Cayley graphs. In this talk, we study pretty good state transfer on Cayley graphs over dihedral groups. By using the representations of dihedral groups, we show that if n is a power of 2, then Cay(Dn, S ) exhibits pretty good state transfer for some subset S in Dn, some concrete constructions are provided. We also show that this is basically the only case for a non-integral Cayley graph Cay(Dn, S ) to have PGST. We note that our methods apply to Cayley graphs over other non-abelian groups such as generalized quaternion groups Q4m, generalized dihedral groups Dnh, bicyclic groups and so on.

    组织单位:数学与金融学院


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