Operator monotones, the reduction criterion and the relative entropy

Abstract

We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we prove a new lower bound on the relative entropy of entanglement and other properties of entanglement measures.

Final version accepted for publication, added references in reference [1] and [13]

References in corpus (1)

• The Holevo bound and Landauer's principle

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