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The Wigner-Yanase skew information was proposed to quantify the informationcontained in quantum states with respect to a conserved additive quantity, andit was later extended to the Wigner-Yanase-Dyson skew informations. Recently,the Wigner-Yanase-Dyson skew informations have been recognized as validresource measures for the resource theory of asymmetry, and their propertieshave been investigated from a resource-theoretic perspective. TheWigner-Yanse-Dyson skew informations have been further generalized to a classcalled metric-adjusted skew informations, and this general family of skewinformations have also been found to be valid asymmetry monotones. Here, weanalyze this general family of the skew informations from an operational pointof view by utilizing the fact that they are valid asymmetry resource monotones.We show that such an approach allows for clear physical meanings as well assimple proofs of some of the basic properties of the skew informations.Notably, we constructively prove that any type of skew information cannot besuperadditive, where the violation of the superadditivity had been only knownfor a specific class of skew informations with numerical counterexamples. Wefurther show a weaker version of superadditivity relation applicable to thegeneral class of the skew informations, which proves a conjecture made for theWigner-Yanase skew information as a special case. We finally discuss anapplication of our results for a situation where quantum clocks are distributedto multiple parties.

Skew informations from an operational view via resource theory of asymmetry