Concepedia

Sufficiency and relative entropy in ∗-algebras with applications in quantum systems

Fumio Hiai, Masanori Ohya, Makoto Tsukada

Pacific Journal of Mathematics · 1983 · 43 citations · 46 references

Open access

Abstract

The sufficiency and weak sufficiency in * -algebras are discussed. Some properties are studied concerning the relative entropy and the sufficiency for invariant states and KMS states in W* and C*-dynamical systems.

References

46

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Engineering, Information Theory, Data Science +4

Conditional expectation in an operator algebra. IV. Entropy and information

Hisaharu Umegaki · Kodai Mathematical Journal · 1962 · 659 citations

Introduction.the Theory, Engineering, Information Theory +12

Conditional expectations in von Neumann algebras

Masamichi Takesaki · Journal of Functional Analysis · 1972 · 475 citations

Expectation Formation, Integrable Probability, Probability Theory +2

Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory

Armin Uhlmann · Communications in Mathematical Physics · 1977 · 413 citations

Dirichlet Form, Engineering, Interpolation Space +6

Relative Entropy for States of von Neumann Algebras II

Huzihiro Araki · Publications of the Research Institute for Mathematical Sciences · 1977 · 354 citations · Full text

Engineering, Representation Theory, Non-faithful Functionals +7