On a correspondence between regular and non-regular operator monotone functions

TL;DR

This paper establishes a bijective relationship between regular and non-regular operator monotone functions and applies this to prove the monotonicity of functions related to quantum information measures.

Contribution

It introduces a novel bijection between regular and non-regular operator monotone functions and provides a new proof for the monotonicity of functions linked to Wigner-Yanase-Dyson information.

Findings

Established a bijection between regular and non-regular operator monotone functions

Provided a new proof of operator monotonicity for certain quantum information functions

Enhanced understanding of the structure of operator monotone functions

Abstract

We prove that there is a bijection between the families of regular and non-regular operator monotone functions. As an application we give a new proof of the operator monotonicity of a certain class of functions related to Wigner-Yanase-Dyson skew information.