  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.
