Introduction to Quantum Information Science by Masahito Hayashi Satoshi Ishizaka Akinori Kawachi Gen Kimura & Tomohiro Ogawa

Author:Masahito Hayashi, Satoshi Ishizaka, Akinori Kawachi, Gen Kimura & Tomohiro Ogawa
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

6.2.6 -Divergence

For each convex function , we can define an information quantity so called the -divergence [16], which constitutes a family of information quantities including the divergence and other important quantities. Various properties of the divergence presented in the previous subsection are proved here as those of the -divergences.

For a convex function (see Appendix A.4) the -divergence is defined by

(6.14)

where we treat which occurs in or in the same way as Remark 6.1. For example, if , we have

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