  We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew
information and modified weighted generalized Wigner-Yanase-Dyson (MWGWYD) skew
information. By revisiting state-channel interaction based on MGWYD skew
information, a family of coherence measures with respect to quantum channels is
proposed. Furthermore, explicit analytical expressions of these coherence
measures of qubit states are derived with respect to different quantum
channels. Moreover, complementarity relations based on MGWYD skew information
and MWGWYD skew information are also presented. Specifically, the conservation
relations are investigated, while two interpretations of them including
symmetry-asymmetry complementarity and wave-particle duality have been
proposed.
