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

DOI10.2140/pjm.1983.107.117zbMath0524.46044OpenAlexW2005648213MaRDI QIDQ585519

Masanori Ohya, Fumio Hiai, Makoto Tsukada

Publication date: 1983

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1983.107.117

zbMATH Keywords

conditional expectationKMS statesKMS conditionGibbs states of quantum lattice systemsinvariant statesone-parameter automorphism grouprelative entropy in *-algebrasweak sufficiency of positive linear maps between *-algebras

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Noncommutative dynamical systems (46L55) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) States of selfadjoint operator algebras (46L30) Sufficiency and information (62B99)

Related Items (11)

On the relative entropy ⋮ Sufficient subalgebras and the relative entropy of states of a von Neumann algebra ⋮ Large Deviation Strategy for Inverse Problem II ⋮ Sufficiency and strong commutants in quantum probability theory ⋮ The quantum relative entropy as a rate function and information criteria ⋮ Quantum Rényi divergences and the strong converse exponent of state discrimination in operator algebras ⋮ Relative Hamiltonians which are not bounded from above ⋮ Some aspects of quantum information theory and their applications to irreversible processes ⋮ The proper formula for relative entropy and its asymptotics in quantum probability ⋮ Continuity of entropy and mutual entropy in C*-dynamical systems ⋮ Noncommutative extension of an integral representation theorem of entropy

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