Trace inequalities on a generalized Wigner–Yanase skew 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. In addition, several trace inequalities on our generalized Wigner–Yanase skew information are argued.