Application of quantum Pinsker inequality to quantum communications

TL;DR

This paper surveys the historical development and significance of quantum relative entropy and quantum Pinsker inequality in quantum communication, highlighting their mathematical foundations and contributions to quantum information science.

Contribution

It provides a comprehensive overview of the contributions of Ikehara and Umegaki Group to quantum information theory, emphasizing their impact on quantum communication design.

Findings

Quantum Pinsker inequality relates quantum relative entropy to trace distance.

Historical analysis of Umegaki's work in quantum information science.

Connection between pure mathematics and practical quantum communication applications.

Abstract

Back in the 1960s, based on Wiener's thought, Shikao Ikehara (first student of N.Wiener) encouraged the progress of Hisaharu Umegaki's research from a pure mathematical aspect in order to further develop the research on mathematical methods of quantum information at Tokyo Institute of Technology. Then, in the 1970s, based on the results accomplished by Umegaki Group, Ikehara instructed the author to develop and spread quantum information science as the global information science. While Umegaki Group's results have been evaluated as major achievements in pure mathematics, their contributions to current quantum information science have not been fully discussed. This paper gvies a survey of my talk in the memorial seminar on Ikehara, in which Ikehara and Umegaki Group's contributions to design theory of quantum communication have been introduced with specific examples such as quantum relative entropy and quantum Pinsker inequality.