Maximum Shannon entropy, minimum Fisher information, and an elementary game

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	Maximum Shannon entropy, minimum Fisher information, and an elementary game
	Luo, SL
	2002-11-01
发表期刊	FOUNDATIONS OF PHYSICS
ISSN	0015-9018
卷号	32 期号:11 页码:1757-1772
摘要	We formulate an elementary statistical game which captures the essence of some fundamental quantum experiments such as photon polarization and spin measurement. We explore and compare the significance of the principle of maximum Shannon entropy and the principle of minimum Fisher information in solving such a game. The solution based on the principle of minimum Fisher information coincides with the solution based on an invariance principle, and provides an informational explanation of Malus law for photon polarization. There is no solution based on the principle of maximum Shannon entropy. The result demonstrates the merits of Fisher information, and the demerits of Shannon entropy, in treating some fundamental quantum problems. It also provides a quantitative example in support of a general philosophy: Nature intends to hide Fisher information, while obeying some simple rules.
关键词	Shannon entropy Fisher information game against nature binary probability Malus' law
语种	英语
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000179770600006
出版者	KLUWER ACADEMIC/PLENUM PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17020
专题	应用数学研究所
通讯作者	Luo, SL
作者单位	1.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.City Univ Hong Kong, Liu Bie Ju Ctr Math Sci, Kowloon, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Luo, SL. Maximum Shannon entropy, minimum Fisher information, and an elementary game[J]. FOUNDATIONS OF PHYSICS,2002,32(11):1757-1772.
APA	Luo, SL.(2002).Maximum Shannon entropy, minimum Fisher information, and an elementary game.FOUNDATIONS OF PHYSICS,32(11),1757-1772.
MLA	Luo, SL."Maximum Shannon entropy, minimum Fisher information, and an elementary game".FOUNDATIONS OF PHYSICS 32.11(2002):1757-1772.