Perturbation theory of von Neumann entropy

doi:10.1088/1674-1056/19/4/040308

Abstract In quantum information theory, von Neumann entropy plays an important role; it is related to quantum channel capacities. Only for a few states can one obtain their entropies. In a continuous variable system, numeric evaluation of entropy is not easy due to infinite dimensions. We develop the perturbation theory for systematically calculating von Neumann entropy of a non-degenerate system as well as a degenerate system.

Keywords: von Neumann entropy perturbation degenerate state

Received: 11 April 2009
Revised: 05 June 2009
Accepted manuscript online:

PACS:	03.65.Fd	(Algebraic methods)
	03.67.-a	(Quantum information)
	02.10.Yn	(Matrix theory)
	02.10.Ud	(Linear algebra)
	02.30.Tb	(Operator theory)

Fund: Project supported by the National Natural Science Foundation of China (Grant No.~60972071), Science and Technology Program of Zhejiang Province, China (Grant No.~2009C31060).

Cite this article:

Chen Xiao-Yu(陈小余) Perturbation theory of von Neumann entropy 2010 Chin. Phys. B 19 040308

[1]	Schumacher B 1995 Phys. Rev. A 51 2738
[2]	Holevo A S 1998 Russian Math. Surveys 53 1295
[2a]	Holevo A S arXiv.org/quant-ph/9808023
[3]	Schumacher B and Westmorland M D 1997 Phys. Rev. A 56 131
[4]	Devetak I 2005 IEEE Trans. Inf. Theory 51 44
[5]	Barnum H, Knill M and Nielsen M A 2000 IEEE Trans. Inf. Theory 46 1317
[6]	Gao Y F, Feng J and Wang J S 2005 Chin. Phys. 14 980
[7]	Zhu X and Tong P Q 2008 Chin. Phys. B 17 1623
[8]	Reed M and Simon B 1978 Methods of Mathematical Physics; Vol.4, Analysis of Operators (New York: Academic Press)
[9]	Vedral V, Plenio M B, Jacobs K and Knight P L 1997 Phys. Rev. A 56 4452
[10]	Chen X Y 2009 J. Phys. B 42 075502

[1]	Simulation of detection and scattering of sound waves by the lateral line of a fish V M Adamyan, I Y Popov, I V Blinova, and V V Zavalniuk. Chin. Phys. B, 2022, 31(2): 024301.
[2]	Stochastic optimal control for norovirus transmission dynamics by contaminated food and water Anwarud Din and Yongjin Li(黎永锦). Chin. Phys. B, 2022, 31(2): 020202.
[3]	Identification of unstable individuals in dynamic networks Dongli Duan(段东立), Tao Chai(柴涛), Xixi Wu(武茜茜), Chengxing Wu(吴成星), Shubin Si(司书宾), and Genqing Bian(边根庆). Chin. Phys. B, 2021, 30(9): 090501.
[4]	Breather solutions of modified Benjamin-Bona-Mahony equation G T Adamashvili. Chin. Phys. B, 2021, 30(2): 020503.
[5]	Dynamics analysis of a 5-dimensional hyperchaotic system with conservative flows under perturbation Xuenan Peng(彭雪楠), Yicheng Zeng(曾以成), and Qi Xie(谢奇). Chin. Phys. B, 2021, 30(10): 100502.
[6]	Identification of key residues in protein functional movements by using molecular dynamics simulations combined with a perturbation-response scanning method Jun-Bao Ma(马君宝), Wei-Bu Wang(王韦卜), and Ji-Guo Su(苏计国). Chin. Phys. B, 2021, 30(10): 108701.
[7]	Growth induced buckling of morphoelastic rod in viscous medium Yitong Zhang(张一桐), Shuai Zhang(张帅), Peng Wang(王鹏). Chin. Phys. B, 2020, 29(5): 054501.
[8]	The (3+1)-dimensional generalized mKdV-ZK equation for ion-acoustic waves in quantum plasmas as well as its non-resonant multiwave solution Xiang-Wen Cheng(程香雯), Zong-Guo Zhang(张宗国), and Hong-Wei Yang(杨红卫). Chin. Phys. B, 2020, 29(12): 124501.
[9]	Dependence of photoelectron-momentum distribution of H₂⁺ molecule on orientation angle and laser ellipticity Hong-Dan Zhang(张宏丹), Si-Qi Zhang(张思琪), Lei Ji(纪磊), Qi Zhen(甄琪), Jing Guo(郭静), Xue-Shen Liu(刘学深). Chin. Phys. B, 2019, 28(5): 053201.
[10]	Discrete symmetrical perturbation and variational algorithm of disturbed Lagrangian systems Li-Li Xia(夏丽莉), Xin-Sheng Ge(戈新生), Li-Qun Chen(陈立群). Chin. Phys. B, 2019, 28(3): 030201.
[11]	Numerical simulation on modulational instability of ion-acoustic waves in plasma Yi-Rong Ma(马艺荣), Lie-Juan Li(李烈娟), Wen-Shan Duan(段文山). Chin. Phys. B, 2019, 28(2): 025201.
[12]	Effect of transient space-charge perturbation on carrier transport in high-resistance CdZnTe semiconductor Yu Guo(郭玉), Gang-Qiang Zha(查钢强), Ying-Rui Li(李颖锐), Ting-Ting Tan(谭婷婷), Hao Zhu(朱昊), Sen Wu(吴森). Chin. Phys. B, 2019, 28(11): 117201.
[13]	Enhancing von Neumann entropy by chaos in spin-orbit entanglement Chen-Rong Liu(刘郴荣), Pei Yu(喻佩), Xian-Zhang Chen(陈宪章), Hong-Ya Xu(徐洪亚), Liang Huang(黄亮), Ying-Cheng Lai(来颖诚). Chin. Phys. B, 2019, 28(10): 100501.
[14]	Effects of resonant magnetic perturbation on the instability of single tearing mode with non-shear flow Le Wang(王乐), Ming Yang(阳明), Wen-Bin Lin(林文斌). Chin. Phys. B, 2019, 28(1): 015203.
[15]	Ground-state energy of beryllium atom with parameter perturbation method Feng Wu(吴锋), Lijuan Meng(孟丽娟). Chin. Phys. B, 2018, 27(9): 093101.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Perturbation theory of von Neumann entropy

Cite this article:

Online attention