﻿ PT-对称量子理论中的量子测量 Quantum Measurement of PT-Symmetric Quantum Theory

Vol.05 No.04(2016), Article ID:19124,8 pages
10.12677/AAM.2016.54091

Quantum Measurement of PT-Symmetric Quantum Theory

Lili Yang, Zhengli Chen, Haipeng Sun

School of Mathematics and Information Science, Shaanxi Normal University (SNNU), Xi’an Shaanxi

Received: Nov. 11th, 2016; accepted: Nov. 26th, 2016; published: Nov. 30th, 2016

ABSTRACT

Quantum computer is a kind of physical device which carries out mathematical and logical calculations, and stores and manages the quantum information efficiently under the rule of the quantum mechanics. Quantum measurement is an important research topic in quantum information and quantum computing realm, however, the relative research has not appeared in the PT-symme- trical quantum system. In this paper, we give the general concept of quantum measurement in the PT-symmetrical quantum system. Moreover, the detailed discussion is described by using the methods of matrix and operation theory, and we obtain two results about quantum measurement in the PT-symmetrical quantum system.

Keywords:PT-Frame, PT-Symmetry, CPT-Frame, States, Measurement

PT-对称量子理论中的量子测量

1. 引言

2. PT-对称性

PT对称理论研究的是量子系统关于“空间对称变换”与“时间反演变换”的对称性。这两种变换是状态空间上的两个算子，它们的定义是

(1)是恒等的线性算子，是共轭线性算子；

(2) (K上的恒等算子)；

(3)

(4)为线性算子，

(5)关于上的原来内积是正定的：即，且

(6)，即，有，则称算子组为算子的一个-框架。

3. PT-对称量子系统中的量子测量

。即

，即

。设，则

(2) 因为

，则的一个CPT-框架，而且为这个PT-对称量子系统的一组测量算子。

，即

。设，则

(2)

4. 结论

Quantum Measurement of PT-Symmetric Quantum Theory[J]. 应用数学进展, 2016, 05(04): 790-797. http://dx.doi.org/10.12677/AAM.2016.54091

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