统计与数据科学学院
---------------------------------------------
学术讲座
讲座题目：Two- and three-uniform states from irredundant orthogonal arrays
讲座 人：庞善起教授，河南师范大学数学与信息科学学院
时 间：2019年5月16日（周四）11:00
地 点：统计与数据科学学院116教室
摘 要：A pure quantum state of N subsystems, each with d levels, is said to be k-uniform if all of its reductions to k qudits are maximally mixed. Only the uniform states obtained from orthogonal arrays (OAs) are considered throughout this work. The Hamming distances of OAs are specially applied to the theory of quantum information. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant orthogonal arrays (IrOAs), then answer the open questions of whether there exist 3-uniform states of N qubits and 2-uniform states of N qutrits, and whether 3-uniform states of qudits (d > 2) for high values of N can be explicitly constructed. In fact, we obtain 3-uniform states for an arbitrary number of N ≥ 8 qubits and 2-uniform states of N qutrits for every N ≥ 4. Additionally, we provide explicit constructions of the 3-uniform states of N ≥ 8 qutrits, N = 6 and N ≥ 8 ququarts and ququints, N ≥ 6 qudits having d levels for any prime power d > 6, and N = 8 and N ≥ 12 qudits having d levels for non-prime-power d ≥ 6. Moreover, we describe an explicit construction scheme for the 2-uniform states of qudits having d ≥ 4 levels. The proofs of existence of the 2-uniform states of N ≥ 6 qubits are simplified by using a class of OAs. Two special 3-uniform states are obtained from IrOA(32, 10, 2, 3) and IrOA(32, 11, 2, 3) using the interaction column property of OAs.
讲座人简介：庞善起，西安电子科技大学博士，河南师范大学数学与信息科学学院教授、博导、副院长，新乡市人大常委会副主任，民盟新乡市委主委，河南省学术和技术带头人，省级重点学科学术带头人。长期从事应用统计和正交表设计及应用研究，主持国家自然科学基金面上项目3项，并将研究成果应用到粉煤灰处理的工业工程中，直接经济效益增加3000万元，间接效益上亿元，研究成果获“河南省科学技术进步奖”。
邀请人：刘民千教授
欢迎广大师生参加！
统计与数据科学学院