Generalized Wigner-Yanase skew information and generalized fisher information

We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum uncertainty quantity excluding the classical mixture. And we introduce a generalized Fisher information and then derive a generalized Cramer-Rao inequality. We also give an example for our generalized Fisher information and then derive the uncertainty relation for two observables.