多体量子系统密度矩阵的表示

吉林大学学报(理学版)

多体量子系统密度矩阵的表示

丁巍巍, 陶元红, 李嫦娥

延边大学理学院数学系, 吉林延吉 133002

收稿日期:2012-12-10 出版日期:2013-09-26 发布日期:2013-09-17
通讯作者: 陶元红 E-mail:taoyuanhong12@126.com

Representations of Density Matrix of a Multipartite Quantum System

DING Weiwei, TAO Yuanhong, LI Chang e

Department of Mathematics, College of Sciences, Yanbian University, Yanji 133002, Jilin Province, China

Received:2012-12-10 Online:2013-09-26 Published:2013-09-17
Contact: TAO Yuanhong E-mail:taoyuanhong12@126.com

摘要/Abstract

摘要：

利用特殊酉群SU(3)的典型生成元及其性质构造矩阵空间M_R(C)的一组Hamel基, 并给出其线性无关性的证明；利用特殊酉群SU(R)的典型生成元构造矩阵空间M_R1R2…_Rn(C)的两组Hamel基, 并在这两组基底下描述了多体量子系统密度矩阵的表示.

关键词: 特殊酉群, 密度矩阵, 多体量子系统, Hamel基

Abstract:

With the help of the typical generators of special unitary group SU(3) and their properties, a Hamel basis of matrix space M_R(C) was constructed, and its linear independence was proved in detail. Next, using the typical generators of special unitary group SU(R), two Hamel bases of matrix space M_R1R2…_Rn(C) were established, under which a representation of density matrix of a multipartite quantum system was presented, thus providing a theoretical basis for studying quantum entanglement.

Key words: special unitary group, density matrix, multipartite quantum system, Hamel basis

中图分类号:

O177.3

丁巍巍, 陶元红, 李嫦娥. 多体量子系统密度矩阵的表示[J]. 吉林大学学报(理学版), 2013, 51(05): 831-835.

DING Weiwei, TAO Yuanhong, LI Chang e. Representations of Density Matrix of a Multipartite Quantum System[J]. Journal of Jilin University Science Edition, 2013, 51(05): 831-835.