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

作者: 杨丽丽 , 陈峥立 , 孙海鹏 :陕西师范大学数学与信息科学学院,陕西 西安;

关键词: PT-框架PT-对称CPT-框架测量PT-Frame PT-Symmetry CPT-Frame States Measurement

摘要: 量子计算机是一类遵循量子力学规律进行高速数学和逻辑运算、存储及处理量子信息的物理装置,量子测量是量子信息和量子计算中的一类重要研究课题,但是在PT-对称量子系统中还没有相关的研究。本文给出PT-对称量子系统中一般量子测量的概念,并运用矩阵和算子论的方法,对这个问题进行了详细的讨论,得到了PT-对称量子系统中关于量子测量的两个结果。

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.

文章引用: 杨丽丽 , 陈峥立 , 孙海鹏 (2016) PT-对称量子理论中的量子测量。 应用数学进展, 5, 790-797. doi: 10.12677/AAM.2016.54091

参考文献

[1] Nielsen, M.A. and Chuang, I.L. 量子计算和量子信息 [M]. 赵平川, 译. 北京: 清华大学出版社, 2004: 79-81.

[2] Bender, C.M., Boettcher, S. (1998) Real Spectra in Non-Hermitian Hamiltonians Having PT-Symmetric. Physical Review Letters, 80, 5243-5246.
https://doi.org/10.1103/PhysRevLett.80.5243

[3] Bender, C.M. (2005) Introduction to PT-Symmetric Quantum Theory. Contemporary Physics, 46, 277-292.
https://doi.org/10.1080/00107500072632

[4] Bender, C.M. and Wu, J.D. (2012) PT-symmetric Scientic. Mathematics of Operations Research, 2, 1-6.

[5] Bender, C.M., Brody, D.C. and Jones, H.F. (2002) Complex Extention of Quantum Mechanics. Physical Review Letters, 89, 617-628.
https://doi.org/10.1103/PhysRevLett.89.270401

[6] Bender, C.M. and Klevansky, S.P. (2010) Families of Particles with Different Masses in PT-Symmetric Quantum Field Theory. Physical Review Letters, 105, 031601.
https://doi.org/10.1103/PhysRevLett.105.031601

[7] Croke, S. (1973) PT-Symmetric Hamiltonians and Their Application in Quantum. Physical Review A, 91, 052113.
https://doi.org/10.1103/PhysRevA.91.052113

[8] Wang, Q., Chia, S. and Zhang, J. (2010) PT-Symmetric as a Generalization of Hermiticity. Journal of Physics A: Mathematical and Theoretical, 43, 38FT02.

[9] Chen, S.L., Chen, C.Y. and Chen, Y.N. (2014) Increase of Entanglement by Local PT-Symmetric Operation. Physical Review Letters, 90, 054301.

[10] Leclerc, A., Viennot, D. and Jolicard, G. (2012) The Role of the Geometric Phases in Adiabatic Population Tracking for non-Hermitian Hamiltonians. Journal of Physics A: Mathematical and Theoretical, 45, 444015.

[11] Cao, H.X., Guo, Z.H. and Chen, Z.L. (2013) CPT-Frames for Non-Hermitian Hamiltonians. Communications in Theoretical Physics, 60, 328-334.
https://doi.org/10.1088/0253-6102/60/3/12

[12] 段媛媛, 刘晓华, 陈峥立. 关于PT-对称的一些研究[J]. 纺织高校基础科学学报, 2013(26): 441-444.

[13] 刘晓华, 陈峥立, 段媛媛. PT-对称中量子态的区分[J]. 计算机工程与应用, 2013, 51(7): 61-63.

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