An axiomatic characterization of a two-parameter extended relative entropy
نویسندگان
چکیده
منابع مشابه
An axiomatic characterization of a two-parameter extended relative entropy
Shannon entropy [1] is one of fundamental quantities in classical information theory and uniquely determinded by the Shannon-Khinchin axiom or the Faddeev axiom. Oneparameter extensions for Shannon entropy have been studied by many researchers [2]. The Rényi entropy [3] and the Tsallis entropy [4] are famous. In the paper [5], the uniqueness theorem for the Tsallis entropy was proven. See also ...
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Shannon entropy [1] is one of fundamental quantities in classical information theory and uniquely determinded by the Shannon-Khinchin axiom or the Faddeev axiom. One-parameter extensions for Shannon entropy have been studied by many researchers. The Rényi entropy [2] and the Tsallis entropy [3] are famous. In the paper [4], the uniqueness theorem for the Tsallis entropy was proved. Also, in our...
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Building upon work by Matsumoto, we show that the quantum relative entropy with full-rank second argument is determined by four simple axioms: (i) Continuity in the first argument; (ii) the validity of the data-processing inequality; (iii) additivity under tensor products; and (iv) super-additivity. This observation has immediate implications for quantum thermodynamics, which we discuss. Specif...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2010
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.3525917