Monotonicity of skew information and its applications in quantum resource theory

We give an alternative proof of skew information via operator algebra approach and show its strong monotonicity under particular quantum TPCP maps. We then formulate a family of new resource measure if the resource can be characterized by a resource destroying map and the free operation should be also modified. Our measure is easy-calculating and applicable to the coherence resource theory as well as quantum asymmetry theory. The operational interpretation needs to be further investigated.