Metric adjusted skew information: Convexity and restricted forms of superadditivity

TL;DR

This paper provides an elementary proof of the convexity of metric adjusted skew information, extends superadditivity results to general cases, and relates recent WYD-information extensions to metric adjusted skew information.

Contribution

It offers a simple proof of convexity, extends superadditivity to broader classes, and connects recent WYD-information extensions to metric adjusted skew information.

Findings

Elementary proof of convexity of metric adjusted skew information

Extension of superadditivity to general metric adjusted skew informations

Relation of WYD-information extensions to metric adjusted skew information

Abstract

We give a truly elementary proof of the convexity of metric adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric adjusted skew informations. Recently, Luo and Zhang introduced the notion of semi-quantum states on a bipartite system and proved superadditivity of the Wigner-Yanase-Dyson skew informations for such states. We extend this result to general metric adjusted skew informations. We finally show that a recently introduced extension to parameter values $ 1<p\le 2 $ of the WYD-information is a special case of (unbounded) metric adjusted skew information.