The author is currently Professor Emeritus at Tohoku University.

“The presentation of this monograph is very friendly, since it is addressed to a large audience made up of mathematicians and physicists, with a generous set of appendices on the basics of von Neumann algebras, positive self-adjoint operators (unbounded) in Hilbert spaces, operator convex functions on (0, 1), and operator connections with normal positive forms. It gathers updated information on f-divergences and it is very useful for specialists, although not exclusively.” (Aurelian Gheondea, Mathematical Reviews, October, 2022)“The contents of the book presents very interesting topics for quantum information scientists … . I would like to recommend this book for two kinds of special groups of scientists: pure mathematicians, who want to learn the power of quantum computing, and quantum information theorists, who are tired of quantum computing. … this book will be a good guide. For the second group, including people like me, this book stimulates the dormant instincts about quantum information theory.” (Kabgyun Jeong, zbMATH 1476.81004, 2022)

• 1 Introduction.- 2 Standard f -Divergences.- 3 Rényi Divergences and Sandwiched Rényi Divergences.- 4 Maximal f -Divergences.- 5 Measured f -Divergences.- 6 Reversibility and Quantum Divergences.- 7 Reversibility and Measurements.- 8 Preservation of Maximal f -Divergences.- A Preliminaries on von Neumann Algebras.- B Preliminaries on Positive Self-Adjoint Operators.- C Operator Convex Functions on (0,1).- D Operator Connections of Normal Positive Functionals.

The author is currently Professor Emeritus at Tohoku University.

“The presentation of this monograph is very friendly, since it is addressed to a large audience made up of mathematicians and physicists, with a generous set of appendices on the basics of von Neumann algebras, positive self-adjoint operators (unbounded) in Hilbert spaces, operator convex functions on (0, 1), and operator connections with normal positive forms. It gathers updated information on f-divergences and it is very useful for specialists, although not exclusively.” (Aurelian Gheondea, Mathematical Reviews, October, 2022)“The contents of the book presents very interesting topics for quantum information scientists … . I would like to recommend this book for two kinds of special groups of scientists: pure mathematicians, who want to learn the power of quantum computing, and quantum information theorists, who are tired of quantum computing. … this book will be a good guide. For the second group, including people like me, this book stimulates the dormant instincts about quantum information theory.” (Kabgyun Jeong, zbMATH 1476.81004, 2022)

• 1 Introduction.- 2 Standard f -Divergences.- 3 Rényi Divergences and Sandwiched Rényi Divergences.- 4 Maximal f -Divergences.- 5 Measured f -Divergences.- 6 Reversibility and Quantum Divergences.- 7 Reversibility and Measurements.- 8 Preservation of Maximal f -Divergences.- A Preliminaries on von Neumann Algebras.- B Preliminaries on Positive Self-Adjoint Operators.- C Operator Convex Functions on (0,1).- D Operator Connections of Normal Positive Functionals.

The author is currently Professor Emeritus at Tohoku University.

“The presentation of this monograph is very friendly, since it is addressed to a large audience made up of mathematicians and physicists, with a generous set of appendices on the basics of von Neumann algebras, positive self-adjoint operators (unbounded) in Hilbert spaces, operator convex functions on (0, 1), and operator connections with normal positive forms. It gathers updated information on f-divergences and it is very useful for specialists, although not exclusively.” (Aurelian Gheondea, Mathematical Reviews, October, 2022)“The contents of the book presents very interesting topics for quantum information scientists … . I would like to recommend this book for two kinds of special groups of scientists: pure mathematicians, who want to learn the power of quantum computing, and quantum information theorists, who are tired of quantum computing. … this book will be a good guide. For the second group, including people like me, this book stimulates the dormant instincts about quantum information theory.” (Kabgyun Jeong, zbMATH 1476.81004, 2022)

• 1 Introduction.- 2 Standard f -Divergences.- 3 Rényi Divergences and Sandwiched Rényi Divergences.- 4 Maximal f -Divergences.- 5 Measured f -Divergences.- 6 Reversibility and Quantum Divergences.- 7 Reversibility and Measurements.- 8 Preservation of Maximal f -Divergences.- A Preliminaries on von Neumann Algebras.- B Preliminaries on Positive Self-Adjoint Operators.- C Operator Convex Functions on (0,1).- D Operator Connections of Normal Positive Functionals.