Monotonicity of skew information and its applications in quantum resource theory
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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 need to be further investigated.
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