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 information. 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 the general metric-adjusted skew information. We finally show that a recently introduced extension to parameter values 1 < p ≤ 2 of the WYD-information is a special case of (unbounded) metric-adjusted skew information.
- Metric-adjusted skew information
- Monotone metric
- Wigner-Yanase-Dyson skew information
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics