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Maximum Shannon entropy, minimum Fisher information, and an elementary game
Luo, SL
2002-11-01
Source PublicationFOUNDATIONS OF PHYSICS
ISSN0015-9018
Volume32Issue:11Pages:1757-1772
AbstractWe 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.
KeywordShannon entropy Fisher information game against nature binary probability Malus' law
Language英语
WOS Research AreaPhysics
WOS SubjectPhysics, Multidisciplinary
WOS IDWOS:000179770600006
PublisherKLUWER ACADEMIC/PLENUM PUBL
Citation statistics
Cited Times:16[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/17020
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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