Quantum f-Divergences in von Neumann Algebras : Reversibility of Quantum Operations
2021 ed.
by
Fumio Hiai
Book Details
Format
Paperback / Softback
Book Series
Mathematical Physics Studies
ISBN-10
9813342013
ISBN-13
9789813342019
Edition
2021 ed.
Publisher
Springer Verlag, Singapore
Imprint
Springer Verlag, Singapore
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jan 27th, 2022
Print length
194 Pages
Ksh 14,400.00
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Relative entropy has played a significant role in various fields of mathematics and physics as the quantum version of the Kullback-Leibler divergence in classical theory. Many variations of relative entropy have been introduced so far with applications to quantum information and related subjects. Typical examples are three different classes, called the standard, the maximal, and the measured f-divergences, all of which are defined in terms of (operator) convex functions f on (0,8) and have respective mathematical and information theoretical backgrounds. The a-Rényi relative entropy and its new version called the sandwiched a-Rényi relative entropy have also been useful in recent developments of quantum information.
Quantum divergences are functions of two states (or more generally, two positive linear functionals) on a quantum system and measure the difference between the two states. They are often utilized to address such problems as state discrimination, error correction, and reversibility of quantum operations. In the second half of the monograph, the reversibility/sufficiency theory for quantum operations (quantum channels) between von Neumann algebras via quantum f-divergences is explained, thus extending and strengthening Petz'' previous work.
For the convenience of the reader, an appendix including concise accounts of von Neumann algebras is provided.
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