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Published July 2016 | public
Book Section - Chapter

Exploiting variational formulas for quantum relative entropy

Abstract

The relative entropy is the basic concept underlying various information measures like entropy, conditional entropy and mutual information. Here, we discuss how to make use of variational formulas for measured relative entropy and quantum relative entropy for understanding the additivity properties of various entropic quantities that appear in quantum information theory. In particular, we show that certain lower bounds on quantum conditional mutual information are superadditive.

Additional Information

© 2016 IEEE. We acknowledge discussions with Fernando Brandão, Douglas Farenick and Hamza Fawzi. Most of this work was done while OF was also with the Department of Computing and Mathematical Sciences at CalTech. MT would like to thank the IQIM at CalTech and John Preskill for his hospitality during the time this project was conceived.

Additional details

Created:
August 20, 2023
Modified:
October 20, 2023