Characterization of coherent power of concatenation of quantum channels

Quantum coherence, existing in quantum states, is a very important resource for design and implementation of quantum technologies. Quantum channels that can generate coherence is also an interesting topic and less known results about it. In this paper, we focus mainly on the coherent power of quantum channels and give a operational meaning to the coherent power. Then we characterize the coherent power of concatenation of quantum channels via that of individual channels. In addition, we also propose a new proper coherence measures which is subadditive. Thus coherence measure can be superadditive, additive, or subadditive, up to the specific problems investigated. At the end of this paper, we compare two different definitions of the coherent powers of quantum channels and find that they are not equivalent in general.