Relative Entropy for States of von Neumann Algebras II | Zendy

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Relative Entropy for States of von Neumann Algebras II

Author(s) -

Huzihiro Araki

Publication year - 1977

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195190105

Subject(s) - mathematics , von neumann architecture , von neumann entropy , kullback–leibler divergence , pure mathematics , generalized relative entropy , abelian von neumann algebra , quantum relative entropy , conditional quantum entropy , von neumann algebra , generalization , entropy (arrow of time) , joint quantum entropy , jordan algebra , algebra over a field , mathematical analysis , algebra representation , principle of maximum entropy , quantum , maximum entropy thermodynamics , thermodynamics , quantum discord , physics , quantum mechanics , statistics , quantum entanglement

Relative entropy of two states of a von Neumann algebra is defined in terms of the relative modular operator. The strict positivity, lower semicontinuity, convexity and monotonicity of relative entropy are proved. The Wigner-Yanase-Dyson-Lieb concavity is also proved for general von Neumann algebra.

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