Uncertainty relation associated with a monotone pair skew information

We derive a trace inequality leading to an uncertainty relation based on the monotone pair skew information introduced by Furuichi. As the monotone pair skew information generalizes the Wigner–Yanase–Dyson skew information as well as some other skew information, our result also extends a few known results on the uncertainty relations. Particularly it reduces to that of Luo, Yanagi, and Furuichi et al. in the special cases.