The author is currently Professor Emeritus at Tohoku University.

• 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 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)

The author is currently Professor Emeritus at Tohoku University.

• 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 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)

The author is currently Professor Emeritus at Tohoku University.

• 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 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)