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J4 ›› 2012, Vol. 47 ›› Issue (4): 70-76.

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(A,B)-量子测量

王文华,曹怀信*,李玮   

  1. 陕西师范大学数学与信息科学学院, 陕西 西安 710062
  • 收稿日期:2011-05-23 出版日期:2012-04-20 发布日期:2012-06-28
  • 通讯作者: 曹怀信(1958- ),男,教授,博士生导师,研究方向为算子理论、算子代数、小波分析与量子信息. Email: caohx@snnu.edu.cn
  • 作者简介:王文华(1987- ),女,硕士研究生,研究方向为算子理论. Email: wenhua@stu.snnu.edu.cn
  • 基金资助:

    国家自然科学基金资助项目(10571113,10871224);陕西省自然科学研究计划(2009JM1011)

(A,B)-quantum measurements

WANG Wen-hua, CAO Huai-xin*, LI Wei   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China
  • Received:2011-05-23 Online:2012-04-20 Published:2012-06-28

摘要:

引入了(A,B)-量子测量的概念,建立了(A,B)-量子测量与以A,B为下、上界的g框架之间的等价关系,并得到它的直和与乘积运算的一些性质。引入了(A,B)-量子测量的对偶量子测量与测量框架算子,给出了典型对偶的构造方法,通过(A,B)-量子测量,得到了量子态的重构公式。

关键词: (A,B)-量子测量;g-框架;测量框架算子;重构公式

Abstract:

The concept of a (A,B)-quantum measurement is introduced and discussed. An equivalent relation between (A,B)-quantum measurement and g-frame with lower and upper bounds A and B is established. Some properties of direct sums and multiplications of (A,B)-quantum measurements are obtained. The measure frame operator and the dual quantum measurement of a (A,B)-quantum measurement are introduced and its canonical dual is constructed. Finally, a reconstruction formula of a quantum states is obtained in light of a (A,B)-quantum measurement.

Key words: (A,B)-quantum measurement; g-frame; measure frame operator; reconstruction formula

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