Metric adjusted skew information: Convexity and restricted forms of superadditivity

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.

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References in corpus (6)

• Metric adjusted skew information
• A Matrix Convexity Approach to Some Celebrated Quantum Inequalities
• Uncertainty Principle and Quantum Fisher Information - II
• The Wigner-Yanase entropy is not subadditive
• Uncertainty principle with quantum Fisher information
• Inequalities for quantum skew information

Cited by in corpus (7)

• Some general properties of unified entropies
• Skew informations from an operational view via resource theory of asymmetry
• Relations for certain symmetric norms and anti-norms before and after partial trace
• Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy
• A unified approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information
• WYD-like skew information measures
• Convexity of quasi-entropy type functions: Lieb's and Ando's convexity theorems revisited