Trace inequalities on a generalized Wigner-Yanase skew information

Abstract

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 mixure. In addition, several trace inequalities on our generalized Wigner-Yanase skew information are argued.